Equivariant symplectic homology of Anosov contact structures

被引：0

作者：

Leonardo Macarini

Gabriel P. Paternain

机构：

[1] Universidade Federal do Rio de Janeiro,Instituto de Matemática

[2] University of Cambridge,Department of Pure Mathematics and Mathematical Statistics

来源：

Bulletin of the Brazilian Mathematical Society, New Series | 2012年 / 43卷

关键词：

Anosov contact structure; Reeb flow; equivariant symplectic homology; 53D42; 37D20;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We show that the differential in positive equivariant symplectic homology or linearized contact homology vanishes for non-degenerate Reeb flows with a continuous invariant Lagrangian subbundle (e.g. Anosov Reeb flows). Several applications are given, including obstructions to the existence of these flows and abundance of periodic orbits for contact forms representing an Anosov contact structure.

引用

页码：513 / 527

页数：14

共 10 条

[1]

Abreu M.(2012)Contact homology of good toric contact manifolds Compositio Math. 148 304-334

[2]

Macarini L.(1985)On geodesic flows satisfying the condition (Y) Proc. Steklov Inst. of Math. 167 3-24

[3]

Anosov D.V.(1972)Periodic orbits for hyperbolic flows Amer. J. Math. 94 1-30

[4]

Bowen R.(1993)Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three Invent. Math. 114 515-563

[5]

Hofer H.(1974)Riemannian manifolds with geodesic flow of Anosov type Ann. of Math. 99 1-13

[6]

Klingenberg W.(1972)Anosov flows and the fundamental group Topology 11 147-150

[7]

Plante J.F.(1989)Equivariant Morse theory for starshaped Hamiltonian systems Trans. Amer. Math. Soc. 311 621-655

[8]

Thurston W.P.(1999)Functors and computations in Floer homology with applications. I Geom. Funct. Anal. 9 985-1033

[9]

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[10]

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