Pub Date : 2022-02-01DOI: 10.1142/9789811245039_0006
{"title":"Homology and Cohomology of CW Complexes","authors":"","doi":"10.1142/9789811245039_0006","DOIUrl":"https://doi.org/10.1142/9789811245039_0006","url":null,"abstract":"","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"10 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88930841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-01DOI: 10.1142/9789811245039_0009
{"title":"Čech Cohomology with Values in a Presheaf","authors":"","doi":"10.1142/9789811245039_0009","DOIUrl":"https://doi.org/10.1142/9789811245039_0009","url":null,"abstract":"","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"60 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84870744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-01DOI: 10.1142/9789811245039_0008
{"title":"Presheaves and Sheaves; Basics","authors":"","doi":"10.1142/9789811245039_0008","DOIUrl":"https://doi.org/10.1142/9789811245039_0008","url":null,"abstract":"","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"27 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82318633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-01DOI: 10.1007/978-3-319-46143-4_7
Andrei T. Patrascu
{"title":"Universal Coefficient Theorems","authors":"Andrei T. Patrascu","doi":"10.1007/978-3-319-46143-4_7","DOIUrl":"https://doi.org/10.1007/978-3-319-46143-4_7","url":null,"abstract":"","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"156 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/978-3-319-46143-4_7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72416729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-01DOI: 10.1142/9789811245039_0014
{"title":"Alexander and Alexander–Lefschetz Duality","authors":"","doi":"10.1142/9789811245039_0014","DOIUrl":"https://doi.org/10.1142/9789811245039_0014","url":null,"abstract":"","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"608 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77021128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-01DOI: 10.1142/9789811245039_0010
{"title":"Presheaves and Sheaves; A Deeper Look","authors":"","doi":"10.1142/9789811245039_0010","DOIUrl":"https://doi.org/10.1142/9789811245039_0010","url":null,"abstract":"","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"71 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84294648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-22DOI: 10.2140/agt.2021.21.3019
Zhenkun Li
In this paper we construct gluing maps and cobordism maps for sutured monopole Floer homology.
{"title":"Gluing maps and cobordism maps in sutured monopole and instanton Floer theories","authors":"Zhenkun Li","doi":"10.2140/agt.2021.21.3019","DOIUrl":"https://doi.org/10.2140/agt.2021.21.3019","url":null,"abstract":"In this paper we construct gluing maps and cobordism maps for sutured monopole Floer homology.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"58 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74440447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-06DOI: 10.2140/agt.2023.23.2389
Steven Amelotte, F. Cohen, Y. Luo
We give a refinement of the stable Snaith splitting of the double loop space of a Moore space and use it to construct infinite $v_1$-periodic families of elements of order $p^{r+1}$ in the homotopy groups of mod $p^r$ Moore spaces. For odd primes $p$, our splitting implies that the homotopy groups of the mod $p^{r+1}$ Moore spectrum are summands of the unstable homotopy groups of each mod $p^r$ Moore space.
{"title":"Infinite families of higher torsion in the homotopy groups of Moore spaces","authors":"Steven Amelotte, F. Cohen, Y. Luo","doi":"10.2140/agt.2023.23.2389","DOIUrl":"https://doi.org/10.2140/agt.2023.23.2389","url":null,"abstract":"We give a refinement of the stable Snaith splitting of the double loop space of a Moore space and use it to construct infinite $v_1$-periodic families of elements of order $p^{r+1}$ in the homotopy groups of mod $p^r$ Moore spaces. For odd primes $p$, our splitting implies that the homotopy groups of the mod $p^{r+1}$ Moore spectrum are summands of the unstable homotopy groups of each mod $p^r$ Moore space.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"87 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72970310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-07DOI: 10.2140/agt.2023.23.2347
C. Livingston
The set of isotopy classes of ordered n-component links in the 3-sphere is acted on by the symmetric group via permutation of the components. The intrinsic symmetry group of the link, S(L), is defined to be the set of elements in the symmetric group that preserve the ordered isotopy type of L as an unoriented link. The study of these groups was initiated in 1969, but the question of whether or not every subgroup of the symmetric group arises as an intrinisic symmetry group of some link has remained open. We provide counterexamples; in particular, if n>5, then there does not exist an n-component link L for which S(L) is the alternating group.
{"title":"Intrinsic symmetry groups of links","authors":"C. Livingston","doi":"10.2140/agt.2023.23.2347","DOIUrl":"https://doi.org/10.2140/agt.2023.23.2347","url":null,"abstract":"The set of isotopy classes of ordered n-component links in the 3-sphere is acted on by the symmetric group via permutation of the components. The intrinsic symmetry group of the link, S(L), is defined to be the set of elements in the symmetric group that preserve the ordered isotopy type of L as an unoriented link. The study of these groups was initiated in 1969, but the question of whether or not every subgroup of the symmetric group arises as an intrinisic symmetry group of some link has remained open. We provide counterexamples; in particular, if n>5, then there does not exist an n-component link L for which S(L) is the alternating group.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"10 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89762243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-30DOI: 10.2140/agt.2022.22.3277
M. Hagen, H. Petyt
We use the projection complex machinery of Bestvina--Bromberg--Fujiwara to study hierarchically hyperbolic groups. In particular, we show that if the group has a BBF colouring and its associated hyperbolic spaces are quasiisometric to trees, then the group is quasiisometric to a finite-dimensional CAT(0) cube complex. We deduce various properties, including the Helly property for hierarchically quasiconvex subsets.
{"title":"Projection complexes and quasimedian maps","authors":"M. Hagen, H. Petyt","doi":"10.2140/agt.2022.22.3277","DOIUrl":"https://doi.org/10.2140/agt.2022.22.3277","url":null,"abstract":"We use the projection complex machinery of Bestvina--Bromberg--Fujiwara to study hierarchically hyperbolic groups. In particular, we show that if the group has a BBF colouring and its associated hyperbolic spaces are quasiisometric to trees, then the group is quasiisometric to a finite-dimensional CAT(0) cube complex. We deduce various properties, including the Helly property for hierarchically quasiconvex subsets.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"23 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87098624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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