$S^1$-equivariant symplectic homology and linearized contact homology
By Frederick J. Bourgeois III, A. Oancea. 2012
111 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/9e36994e59b6c5fd645531afe13aa194f440f06c
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The positive equivariant symplectic homology as an invariant for some contact manifolds (2015, methodology): “al induced by (8) that we can formally write as @bS1 = ’ 0 + u 1’ 1 + u 2’ 2 + ::: As before, there are well-dened continuation maps induced by increasing homotopies of Hamiltonians. Proposition 3.2 [5] The S1 equivariant homology of W is given by: SHS1 (W) := lim ! H2H std H SCbS1 (H 0);@bS1 : De”
- Brieskorn manifolds in contact topology (2013, methodology): “c Reeb orbits (dened right after this remark). One can also lter by index and this leads to yet another spectral sequence used by Bourgeois and Oancea in part II of their proof of Proposition 3.7 in [BO4]. We brie y discuss this in Section 8.4) of Appendix C. Denition 5.6. Call a non-degenerate peri”
- Cylindrical contact homology for dynamically convex contact forms in three dimensions (2014, unknown): “nition of CCZ is quite different; it starts with a “Morse-Bott” chain complex with two generators for each (good or bad) Reeb orbit as in [5], and then passes to an S1-equivariant version similarly to [6]. We expect that CHZ agrees with the invariant SHS1 ∗ (Y,ξ) defined in [6, §4.1.2]; the latter is ”