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

@article{Bourgeois2012S1equivariantSH,
  title={\$S^1\$-equivariant symplectic homology and linearized contact homology},
  author={F. Bourgeois and A. Oancea},
  journal={arXiv: Symplectic Geometry},
  year={2012}
}
  • F. Bourgeois, A. Oancea
  • Published 2012
  • Mathematics
  • arXiv: Symplectic Geometry
  • 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. 
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    References

    SHOWING 1-10 OF 65 REFERENCES
    The Gysin exact sequence for $S^1$-equivariant symplectic homology
    • 48
    • PDF
    An exact sequence for contact- and symplectic homology
    • 92
    • PDF
    A FLOER HOMOLOGY FOR EXACT CONTACT EMBEDDINGS
    • 94
    • PDF
    A Morse-Bott approach to contact homology
    • 228
    • PDF
    Symplectic fixed points and holomorphic spheres
    • 468
    Introduction to Symplectic Field Theory
    • 619
    • PDF
    Fredholm theory and transversality for the parametrized and for the S1-invariant symplectic action
    • 26
    • Highly Influential
    • PDF