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

Frédéric Bourgeois (1) , Alexandru Oancea (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 IMJ - Institut de Mathématiques de Jussieu

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, as well as a rigorous definition of cylindrical/linearized contact homology based on an $S^1$-equivariant construction.

Domaines: Géométrie symplectique [math.SG]; Topologie géométrique [math.GT]

Frédéric Bourgeois, Alexandru Oancea. $S^1$-equivariant symplectic homology and linearized contact homology. 2013. ⟨hal-01010943⟩