$S^1$-equivariant symplectic homology and linearized contact homology

Abstract

We present three equivalent definitions of $S^1$-equivariant symplectic homology. We show that, using rational coefficients, the positive part of $S^1$-equivariant symplectic homology is isomorphic to linearized contact homology, when the latter is defined. We present several computations and applications, and introduce a rigorously defined substitute for cylindrical/linearized contact homology based on an $S^1$-equivariant construction.

v3: 67 pages, 1 figure. Version of June 9, 2014. Streamlined exposition and minor changes throughout the text

References in corpus (3)

• Functors and Computations in Floer homology with Applications Part II
• Symplectic cohomology and Viterbo's theorem
• Displaceability and the mean Euler characteristic

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