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Counting embedded curves in symplectic $6$-manifolds 计算折射 $6$-manifolds 中的嵌入曲线
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2023-12-20 DOI: 10.4171/cmh/556
Aleksander Doan, Thomas Walpuski
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引用次数: 0
Erratum to “The cyclic homology of the group rings” 对 "群环的循环同源性 "的勘误
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2023-11-18 DOI: 10.4171/cmh/561
D. Burghelea
{"title":"Erratum to “The cyclic homology of the group rings”","authors":"D. Burghelea","doi":"10.4171/cmh/561","DOIUrl":"https://doi.org/10.4171/cmh/561","url":null,"abstract":"","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":"59 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139262026","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}
引用次数: 0
Erratum to “Ergodic components of partially hyperbolic systems” 对 "部分双曲系统的遍历成分 "的勘误
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2023-11-18 DOI: 10.4171/cmh/560
Andy Hammerlindl
{"title":"Erratum to “Ergodic components of partially hyperbolic systems”","authors":"Andy Hammerlindl","doi":"10.4171/cmh/560","DOIUrl":"https://doi.org/10.4171/cmh/560","url":null,"abstract":"","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":"45 6","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139262426","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}
引用次数: 0
Lagrangian cobordisms and Lagrangian surgery 拉格朗日坐标和拉格朗日手术
3区 数学
Commentarii Mathematici Helvetici Pub Date : 2023-11-03 DOI: 10.4171/cmh/554
Jeff Hicks
{"title":"Lagrangian cobordisms and Lagrangian surgery","authors":"Jeff Hicks","doi":"10.4171/cmh/554","DOIUrl":"https://doi.org/10.4171/cmh/554","url":null,"abstract":"Lagrangian surgery and Lagrangian cobordism give geometric interpretations to exact triangles in Floer cohomology. Lagrangian $k$-surgery modifies an immersed Lagrangian submanifold by topological $k$-surgery while removing a self-intersection point of the immersion. Associated to a $k$-surgery is a Lagrangian surgery trace cobordism. We prove that every Lagrangian cobordism is exactly homotopic to a concatenation of suspension cobordisms and Lagrangian surgery traces. Furthermore, we show that each Lagrangian surgery trace bounds a holomorphic teardrop pairing the Morse cochain associated to the handle attachment with the Floer cochain generated by the self-intersection. We give a sample computation for how these decompositions can be used to algorithmically construct bounding cochains for Lagrangian submanifolds, recover the Lagrangian surgery exact sequence, and provide conditions for when non-monotone Lagrangian cobordisms yield continuation maps in the Fukaya category.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":"221 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135774997","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}
引用次数: 0
Pressure at infinity and strong positive recurrence in negative curvature 无穷远处的压力和负曲率处的强正递归
3区 数学
Commentarii Mathematici Helvetici Pub Date : 2023-10-24 DOI: 10.4171/cmh/552
Sébastien Gouëzel, Camille Noûs, Barbara Schapira, Samuel Tapie, Felipe Riquelme
{"title":"Pressure at infinity and strong positive recurrence in negative curvature","authors":"Sébastien Gouëzel, Camille Noûs, Barbara Schapira, Samuel Tapie, Felipe Riquelme","doi":"10.4171/cmh/552","DOIUrl":"https://doi.org/10.4171/cmh/552","url":null,"abstract":"In the context of geodesic flows of noncompact negatively curved manifolds, we propose three different definitions of entropy and pressure at infinity, through growth of periodic orbits, critical exponents of Poincaré series, and entropy (pressure) of invariant measures. We show that these notions coincide. Thanks to these entropy and pressure at infinity, we investigate thoroughly the notion of strong positive recurrence in this geometric context. A potential is said to be strongly positively recurrent when its pressure at infinity is strictly smaller than the full topological pressure. We show, in particular, that if a potential is strongly positively recurrent, then it admits a finite Gibbs measure. We also provide easy criteria allowing to build such strong positively recurrent potentials and many examples.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135220348","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}
引用次数: 2
Ricci flow of $W^{2,2}$-metrics in four dimensions 四维W^{2,2}$-度量的Ricci流
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2023-09-08 DOI: 10.4171/cmh/553
Tobias Lamm, M. Simon
{"title":"Ricci flow of $W^{2,2}$-metrics in four dimensions","authors":"Tobias Lamm, M. Simon","doi":"10.4171/cmh/553","DOIUrl":"https://doi.org/10.4171/cmh/553","url":null,"abstract":"","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41888105","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}
引用次数: 0
Corrigendum and addendum to Appendix A of “Fractal geometry of the complement of Lagrange spectrum in Markov spectrum” “马尔可夫谱中拉格朗日谱补的分形几何”附录A的勘误和补充
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2023-09-08 DOI: 10.4171/cmh/558
Luke Jeffreys, Carlos Matheus, Carlos Gustavo Moreira, Clément Rieutord
{"title":"Corrigendum and addendum to Appendix A of “Fractal geometry of the complement of Lagrange spectrum in Markov spectrum”","authors":"Luke Jeffreys, Carlos Matheus, Carlos Gustavo Moreira, Clément Rieutord","doi":"10.4171/cmh/558","DOIUrl":"https://doi.org/10.4171/cmh/558","url":null,"abstract":"","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48801169","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}
引用次数: 0
$mathbb{R}$-covered foliations and transverse pseudo-Anosov flows in atoroidal pieces $mathbb{R}$-覆盖叶和横向伪anosov流
3区 数学
Commentarii Mathematici Helvetici Pub Date : 2023-05-23 DOI: 10.4171/cmh/547
Sergio R. Fenley
{"title":"$mathbb{R}$-covered foliations and transverse pseudo-Anosov flows in atoroidal pieces","authors":"Sergio R. Fenley","doi":"10.4171/cmh/547","DOIUrl":"https://doi.org/10.4171/cmh/547","url":null,"abstract":"We study the transverse geometric behavior of 2-dimensional foliations in 3-manifolds. We show that an $mathbb{R}$-covered, transversely orientable foliation with Gromov hyperbolic leaves in a closed 3-manifold admits a regulating, transverse pseudo-Anosov flow (in the appropriate sense) in each atoroidal piece of the manifold. The flow is a blow up of a one prong pseudo-Anosov flow. In addition we show that there is a regulating flow for the whole foliation. We also determine how deck transformations act on the universal circle of the foliation.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135183733","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}
引用次数: 0
Quantitative estimates for the Bakry–Ledoux isoperimetric inequality Bakry-Ledoux等周不等式的定量估计
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2022-01-18 DOI: 10.4171/cmh/523
Cong Hung Mai, Shin-ichi Ohta
{"title":"Quantitative estimates for the Bakry–Ledoux isoperimetric inequality","authors":"Cong Hung Mai, Shin-ichi Ohta","doi":"10.4171/cmh/523","DOIUrl":"https://doi.org/10.4171/cmh/523","url":null,"abstract":"We establish a quantitative isoperimetric inequality for weighted Riemannian manifolds with $operatorname{Ric}_{infty} ge 1$. Precisely, we give an upper bound of the volume of the symmetric difference between a Borel set and a sub-level (or super-level) set of the associated guiding function (arising from the needle decomposition), in terms of the deficit in Bakry–Ledoux’s Gaussian isoperimetric inequality. This is the first quantitative isoperimetric inequality on noncompact spaces besides Euclidean and Gaussian spaces. Our argument makes use of Klartag’s needle decomposition (also called localization), and is inspired by a recent work of Cavalletti, Maggi and Mondino on compact spaces. Besides the quantitative isoperimetry, a reverse Poincaré inequality for the guiding function that we have as a key step, as well as the way we use it, are of independent interest.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":"47 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138540715","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}
引用次数: 0
Curvature of the second kind and a conjecture of Nishikawa 第二类曲率与Nishikawa的一个猜想
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2021-12-02 DOI: 10.4171/cmh/545
M. Gursky, Xiaodong Cao, Hung Tran
{"title":"Curvature of the second kind and a conjecture of Nishikawa","authors":"M. Gursky, Xiaodong Cao, Hung Tran","doi":"10.4171/cmh/545","DOIUrl":"https://doi.org/10.4171/cmh/545","url":null,"abstract":"In this paper, we investigate manifolds for which the curvature of the second kind (following the terminology of Nishikawa) satisfies certain positivity conditions. Our main result settles Nishikawa's conjecture that manifolds for which the curvature (operator) of the second kind are positive are diffeomorphic to a sphere, by showing that such manifolds satisfy Brendle's PIC1 condition. In dimension four we show that curvature of the second kind has a canonical normal form, and use this to classify Einstein four-manifolds for which the curvature (operator) of the second kind is five-non-negative. We also calculate the normal form for some explicit examples in order to show that this assumption is sharp.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42823620","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}
引用次数: 15
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