Pub Date : 2021-01-01DOI: 10.1215/21562261-2021-0003
Kei Irie
We prove two refinements of theC∞-closing lemma for 3-dimensional Reeb flows, which was proved by the author as an application of spectral invariants ofEmbedded Contact Homology (ECH). Specifically, we prove the following two results: (i) for aC∞-generic contact form on any closed 3-manifold, the union of periodic Reeb orbits representing ECH homology classes is dense; (ii) a certain real-analytic version of the C∞-closing lemma for 3-dimensional Reeb flows. A few questions and conjectures related to these results are also discussed.
{"title":"Remarks about the C∞-closing lemma for 3-dimensional Reeb flows","authors":"Kei Irie","doi":"10.1215/21562261-2021-0003","DOIUrl":"https://doi.org/10.1215/21562261-2021-0003","url":null,"abstract":"We prove two refinements of theC∞-closing lemma for 3-dimensional Reeb flows, which was proved by the author as an application of spectral invariants ofEmbedded Contact Homology (ECH). Specifically, we prove the following two results: (i) for aC∞-generic contact form on any closed 3-manifold, the union of periodic Reeb orbits representing ECH homology classes is dense; (ii) a certain real-analytic version of the C∞-closing lemma for 3-dimensional Reeb flows. A few questions and conjectures related to these results are also discussed.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":"-1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66025490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.1215/21562261-2021-0001
Suguru Ishikawa
Our aim here is to explain a new technique for the construction of a smooth Kuranishi structure, which we used in our previous article about the construction of symplectic field theory. We explain this technique in the case of a Morse chain complex.
{"title":"Smooth Kuranishi structure of the space of Morse trajectories","authors":"Suguru Ishikawa","doi":"10.1215/21562261-2021-0001","DOIUrl":"https://doi.org/10.1215/21562261-2021-0001","url":null,"abstract":"Our aim here is to explain a new technique for the construction of a smooth Kuranishi structure, which we used in our previous article about the construction of symplectic field theory. We explain this technique in the case of a Morse chain complex.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":"-1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66025478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-07DOI: 10.1215/21562261-10428532
Y. Kodama
We prove that the braided Thompson group $BV$ has a linear divergence function. By the work of Druţu, Mozes, and Sapir, this leads none of asymptotic cones of $BV$ has a cut-point.
{"title":"Divergence function of the braided Thompson group","authors":"Y. Kodama","doi":"10.1215/21562261-10428532","DOIUrl":"https://doi.org/10.1215/21562261-10428532","url":null,"abstract":"We prove that the braided Thompson group $BV$ has a linear divergence function. By the work of Druţu, Mozes, and Sapir, this leads none of asymptotic cones of $BV$ has a cut-point.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46657278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-01DOI: 10.1215/21562261-2019-0057
Koichi Inoue
{"title":"The conversion formulas between π∗BP and H∗BP","authors":"Koichi Inoue","doi":"10.1215/21562261-2019-0057","DOIUrl":"https://doi.org/10.1215/21562261-2019-0057","url":null,"abstract":"","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":"60 1","pages":"1177-1189"},"PeriodicalIF":0.6,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45466812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-01DOI: 10.1215/21562261-2019-0063
Makoto Nakamura
{"title":"On the nonrelativistic limit of a semilinear field equation in a homogeneous and isotropic space","authors":"Makoto Nakamura","doi":"10.1215/21562261-2019-0063","DOIUrl":"https://doi.org/10.1215/21562261-2019-0063","url":null,"abstract":"","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":"60 1","pages":"1333-1359"},"PeriodicalIF":0.6,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43875057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-01DOI: 10.1215/21562261-2019-0064
Cristian Virdol
{"title":"On Artin’s conjecture for CM elliptic curves","authors":"Cristian Virdol","doi":"10.1215/21562261-2019-0064","DOIUrl":"https://doi.org/10.1215/21562261-2019-0064","url":null,"abstract":"","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":"60 1","pages":"1361-1371"},"PeriodicalIF":0.6,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45890442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-13DOI: 10.1215/21562261-10428437
Y. Nishii
We consider the global Cauchy problem for a two-component system of cubic semilinear wave equations in two space dimensions. We give a criterion for large time non-decay of the energy for small amplitude solutions in terms of the radiation fields associated with the initial data.
{"title":"Nondecay of the energy for a system of semilinear wave equations","authors":"Y. Nishii","doi":"10.1215/21562261-10428437","DOIUrl":"https://doi.org/10.1215/21562261-10428437","url":null,"abstract":"We consider the global Cauchy problem for a two-component system of cubic semilinear wave equations in two space dimensions. We give a criterion for large time non-decay of the energy for small amplitude solutions in terms of the radiation fields associated with the initial data.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47369809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-06DOI: 10.1215/21562261-2022-0040
F. Balacheff, V. Despr'e, H. Parlier
In this article we explore the relationship between the systole and the diameter of closed hyperbolic orientable surfaces. We show that they satisfy a certain inequality, which can be used to deduce that their ratio has a (genus dependent) upper bound.
{"title":"Systoles and diameters of hyperbolic surfaces","authors":"F. Balacheff, V. Despr'e, H. Parlier","doi":"10.1215/21562261-2022-0040","DOIUrl":"https://doi.org/10.1215/21562261-2022-0040","url":null,"abstract":"In this article we explore the relationship between the systole and the diameter of closed hyperbolic orientable surfaces. We show that they satisfy a certain inequality, which can be used to deduce that their ratio has a (genus dependent) upper bound.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47952695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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