$S^1$-equivariant symplectic homology and linearized contact homology
  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. 
Fr\'ed\'eric Bourgeois, Alexandru Oancea
math.SG math.GT