Pub Date : 2021-12-17DOI: 10.15673/tmgc.v14i3.2032
M. Golasiński
A homological criterium from [Golasiński, M., On homotopy nilpotency of loop spaces of Moore spaces, Canad. Math. Bull. (2021), 1–12] is applied to investigate the homotopy nilpotency of some suspended spaces. We investigate the homotopy nilpotency of the wedge sum and smash products of Moore spaces M (A, n) with n ≥ 1. The homotopy nilpotency of homological spheres are studied as well.
{"title":"On homotopy nilpotency of some suspended spaces","authors":"M. Golasiński","doi":"10.15673/tmgc.v14i3.2032","DOIUrl":"https://doi.org/10.15673/tmgc.v14i3.2032","url":null,"abstract":"A homological criterium from [Golasiński, M., On homotopy nilpotency of loop spaces of Moore spaces, Canad. Math. Bull. (2021), 1–12] is applied to investigate the homotopy nilpotency of some suspended spaces. We investigate the homotopy nilpotency of the wedge sum and smash products of Moore spaces M (A, n) with n ≥ 1. The homotopy nilpotency of homological spheres are studied as well.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82000062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-17DOI: 10.15673/tmgc.v14i4.2155
N. Vashpanova, A. Savchenko, N. Vasylieva
The paper treats pseudo-Riemannian spaces permitting generalized φ(Ric)-vector fields. We study conditions for the existence of such vector fields in conformally flat, equidistant, reducible and Kählerian pseudo-Riemannian spaces. The obtained results can be applied for the construction of generalized φ(Ric)-vector fields that differ from φ(Ric)-vector fields. The research is carried out locally without limitations imposed on a sign of metric tensor.
{"title":"Generalized φ(Ric)-vector fields in special pseudo-Riemannian spaces","authors":"N. Vashpanova, A. Savchenko, N. Vasylieva","doi":"10.15673/tmgc.v14i4.2155","DOIUrl":"https://doi.org/10.15673/tmgc.v14i4.2155","url":null,"abstract":"The paper treats pseudo-Riemannian spaces permitting generalized φ(Ric)-vector fields. We study conditions for the existence of such vector fields in conformally flat, equidistant, reducible and Kählerian pseudo-Riemannian spaces. The obtained results can be applied for the construction of generalized φ(Ric)-vector fields that differ from φ(Ric)-vector fields. The research is carried out locally without limitations imposed on a sign of metric tensor.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"66 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81461874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-17DOI: 10.15673/tmgc.v14i4.2140
Володимир Анатолійович Кіосак, Олександр Олегович Пришляк, Олександр Васильович Лесечко
В роботі досліджуються два псевдоріманових простори, які мають спільні геодезичні лінії. Вимагається виконання умов алгебраїчного та диференціального характеру на тензор Рімана одного з них. А операція опускання індексів та обчислення коваріантної похідної здійснюється відносно метрики та об'єктів зв'язності іншого простору. Для досліджень використовується спеціальний допоміжний тензор. Доведено, що виконання додаткових умов приводить до просторів, що не допускають нетривіальних геодезичних відображень, або простори належать до еквідістантних просторів. Використовуються тензорні методи без обмежень на знак метрики.
{"title":"On the geodesic mappings of pseudo-Riemannian spaces with special supplementary tensor","authors":"Володимир Анатолійович Кіосак, Олександр Олегович Пришляк, Олександр Васильович Лесечко","doi":"10.15673/tmgc.v14i4.2140","DOIUrl":"https://doi.org/10.15673/tmgc.v14i4.2140","url":null,"abstract":"В роботі досліджуються два псевдоріманових простори, які мають спільні геодезичні лінії. Вимагається виконання умов алгебраїчного та диференціального характеру на тензор Рімана одного з них. А операція опускання індексів та обчислення коваріантної похідної здійснюється відносно метрики та об'єктів зв'язності іншого простору. Для досліджень використовується спеціальний допоміжний тензор. Доведено, що виконання додаткових умов приводить до просторів, що не допускають нетривіальних геодезичних відображень, або простори належать до еквідістантних просторів. Використовуються тензорні методи без обмежень на знак метрики.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90353338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-27DOI: 10.15673/tmgc.v14i2.2097
Тетяна Iванiвна Шевченко, Тетяна Сергіївна Спічак, Дмитро Миколайович Дойков
The present paper studies the main type of conformal reducible conformally flat spaces. We prove that these spaces are subprojective spaces of Kagan, while Riemann tensor is defined by a vector defining the conformal mapping. This allows to carry out the complete classification of these spaces. The obtained results can be effectively applied in further research in mechanics, geometry, and general theory of relativity. Under certain conditions the obtained equations describe the state of an ideal fluid and represent quasi-Einstein spaces. Research is carried out locally in tensor shape.
{"title":"On conformally reducible pseudo-Riemannian spaces","authors":"Тетяна Iванiвна Шевченко, Тетяна Сергіївна Спічак, Дмитро Миколайович Дойков","doi":"10.15673/tmgc.v14i2.2097","DOIUrl":"https://doi.org/10.15673/tmgc.v14i2.2097","url":null,"abstract":"\u0000The present paper studies the main type of conformal reducible conformally flat spaces. \u0000We prove that these spaces are subprojective spaces of Kagan, while Riemann tensor is defined by a vector defining the conformal mapping. \u0000This allows to carry out the complete classification of these spaces. \u0000The obtained results can be effectively applied in further research in mechanics, geometry, and general theory of relativity. \u0000Under certain conditions the obtained equations describe the state of an ideal fluid and represent quasi-Einstein spaces. \u0000Research is carried out locally in tensor shape. \u0000","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86251199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-05-16DOI: 10.15673/tmgc.v14i1.1936
V. Kiosak, A. Savchenko, O. Latysh
The paper treats geodesic mappings of quasi-Einstein spaces with gradient defining vector. Previously the authors defined three types of these spaces. In the present paper it is proved that there are no quasi-Einstein spaces of special type. It is demonstrated that quasi-Einstein spaces of main type are closed with respect to geodesic mappings. The spaces of particular type are proved to be geodesic $D$-symmetric spaces.
{"title":"Geodesic mappings of compact quasi-Einstein spaces, II","authors":"V. Kiosak, A. Savchenko, O. Latysh","doi":"10.15673/tmgc.v14i1.1936","DOIUrl":"https://doi.org/10.15673/tmgc.v14i1.1936","url":null,"abstract":"\u0000The paper treats geodesic mappings of quasi-Einstein spaces with gradient defining vector. \u0000 \u0000Previously the authors defined three types of these spaces. \u0000In the present paper it is proved that there are no quasi-Einstein spaces of special type. \u0000It is demonstrated that quasi-Einstein spaces of main type are closed with respect to geodesic mappings. \u0000The spaces of particular type are proved to be geodesic $D$-symmetric spaces. \u0000 \u0000 ","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"9 1","pages":"80-91"},"PeriodicalIF":0.0,"publicationDate":"2021-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80572998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-23DOI: 10.15673/TMGC.V13I4.1953
I. Kuznietsova, S. Maksymenko
Let $M$ be a connected compact orientable surface, $f:Mto mathbb{R}$ be a Morse function, and $h:Mto M$ be a diffeomorphism which preserves $f$ in the sense that $fcirc h = f$. We will show that if $h$ leaves invariant each regular component of each level set of $f$ and reverses its orientation, then $h^2$ is isotopic to the identity map of $M$ via $f$-preserving isotopy. This statement can be regarded as a foliated and a homotopy analogue of a well known observation that every reversing orientation orthogonal isomorphism of a plane has order $2$, i.e. a mirror symmetry with respect to some line. The obtained results hold in fact for a larger class of maps with isolated singularities from compact orientable surfaces to the real line and the circle.
设$M$是一个连通紧致可定向曲面，$f:M到mathbb{R}$是一个莫尔斯函数，$h:M到M$是一个在$fcirc h = f$的意义上保持$f$的微分同态。我们将证明，如果$h$使$f$的每个水平集的每个正则分量不变并反转其方向，则$h^2$是通过$f$保持同位素与$M$的恒等映射的同位素。这个命题可以看作是一个众所周知的观察的叶状和同伦的类比，即平面的每一个反转方向正交同构都有阶$2$，即关于某条线的镜像对称。所得结果实际上适用于从紧致可定向曲面到实线和圆的更大一类具有孤立奇点的映射。
{"title":"Reversing orientation homeomorphisms of surfaces","authors":"I. Kuznietsova, S. Maksymenko","doi":"10.15673/TMGC.V13I4.1953","DOIUrl":"https://doi.org/10.15673/TMGC.V13I4.1953","url":null,"abstract":"\u0000Let $M$ be a connected compact orientable surface, $f:Mto mathbb{R}$ be a Morse function, and $h:Mto M$ be a diffeomorphism which preserves $f$ in the sense that $fcirc h = f$. \u0000We will show that if $h$ leaves invariant each regular component of each level set of $f$ and reverses its orientation, then $h^2$ is isotopic to the identity map of $M$ via $f$-preserving isotopy. \u0000This statement can be regarded as a foliated and a homotopy analogue of a well known observation that every reversing orientation orthogonal isomorphism of a plane has order $2$, i.e. a mirror symmetry with respect to some line. \u0000The obtained results hold in fact for a larger class of maps with isolated singularities from compact orientable surfaces to the real line and the circle. \u0000 \u0000 ","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"171 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79401265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-22DOI: 10.15673/tmgc.v14i2.1939
K. Eftekharinasab
We present some transversality results for a category of Frechet manifolds, the so-called MCk - Frechet manifolds. In this context, we apply the obtained transversality results to construct the degree of nonlinear Fredholm mappings by virtue of which we prove a rank theorem, an invariance of domain theorem and a Bursuk-Ulam type theorem.
{"title":"Some applications of transversality for infinite dimensional manifolds","authors":"K. Eftekharinasab","doi":"10.15673/tmgc.v14i2.1939","DOIUrl":"https://doi.org/10.15673/tmgc.v14i2.1939","url":null,"abstract":"We present some transversality results for a category of Frechet manifolds, the so-called MCk - Frechet manifolds. In this context, we apply the obtained transversality results to construct the degree of nonlinear Fredholm mappings by virtue of which we prove a rank theorem, an invariance of domain theorem and a Bursuk-Ulam type theorem.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"95 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81851886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.15673/tmgc.v14i2.2008
Bohdan Feshchenko
In this paper we give an algebraic description of fundamental groups of orbits of circle-valued Morse functions on T2 with respect to the action of the group of diffeomorphisms of T2
本文给出T2上圆值Morse函数的基本轨道群关于T2的微分同态群的作用的代数描述
{"title":"Deformations of circle-valued Morse functions on 2-torus","authors":"Bohdan Feshchenko","doi":"10.15673/tmgc.v14i2.2008","DOIUrl":"https://doi.org/10.15673/tmgc.v14i2.2008","url":null,"abstract":"In this paper we give an algebraic description of fundamental groups of orbits of circle-valued Morse functions on T2 with respect to the action of the group of diffeomorphisms of T2","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"230 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87637335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-27DOI: 10.15673/tmgc.v13i3.1880
Ігор Юрійович Власенко
The paper describes homotopy classes of open continuous functions on finite open topological graphs
研究了有限开拓扑图上开连续函数的同伦类
{"title":"Open finite-to-one functions on open topological graphs","authors":"Ігор Юрійович Власенко","doi":"10.15673/tmgc.v13i3.1880","DOIUrl":"https://doi.org/10.15673/tmgc.v13i3.1880","url":null,"abstract":"\u0000The paper describes homotopy classes of open continuous functions on finite open topological graphs \u0000 \u0000 ","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85364964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-24DOI: 10.15673/tmgc.v13i3.1779
Christian Hatamian, A. Prishlyak
The present paper investigates Heegaard diagrams of non-orientable closed $3$-manifolds, i.e. a non-orienable closed surface together with two sets of meridian disks of both handlebodies. It is found all possible non-orientable genus $2$ Heegaard diagrams of complexity less than $6$. Topological properties of Morse flows on closed smooth non-orientable $3$-manifolds are described. Normalized Heegaard diagrams are furhter used for classification Morse flows with a minimal number of singular points and singular trajectories
{"title":"Heegaard diagrams and optimal Morse flows on non-orientable 3-manifolds of genus 1 and genus $2$","authors":"Christian Hatamian, A. Prishlyak","doi":"10.15673/tmgc.v13i3.1779","DOIUrl":"https://doi.org/10.15673/tmgc.v13i3.1779","url":null,"abstract":"\u0000The present paper investigates Heegaard diagrams of non-orientable closed $3$-manifolds, i.e. a non-orienable closed surface together with two sets of meridian disks of both handlebodies. \u0000It is found all possible non-orientable genus $2$ Heegaard diagrams of complexity less than $6$. \u0000Topological properties of Morse flows on closed smooth non-orientable $3$-manifolds are described. \u0000Normalized Heegaard diagrams are furhter used for classification Morse flows with a minimal number of singular points and singular trajectories \u0000 \u0000 \u0000 ","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91203693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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