An exact sequence for contact- and symplectic homology
Abstract
A symplectic manifold with contact type boundary induces a linearization of the contact homology of with corresponding linearized contact homology . We establish a Gysin-type exact sequence in which the symplectic homology of maps to , which in turn maps to , by a map of degree -2, which then maps to . Furthermore, we give a description of the degree -2 map in terms of rational holomorphic curves with constrained asymptotic markers, in the symplectization of .
Keywords
Cite
@article{arxiv.0704.2169,
title = {An exact sequence for contact- and symplectic homology},
author = {Frédéric Bourgeois and Alexandru Oancea},
journal= {arXiv preprint arXiv:0704.2169},
year = {2015}
}
Comments
Final version. Changes for v2: Proof of main theorem supplemented with detailed discussion of continuation maps. Description of degree -2 map rewritten with emphasis on asymptotic markers. Sec. 5.2 rewritten with emphasis on 0-dim. moduli spaces. Transversality discussion reorganized for clarity (now Remark 9). Various other minor modifications