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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Symplectic and contact differential graded algebras

Tobias Ekholm and Alexandru Oancea

Geometry & Topology 21 (2017) 2161–2230
Abstract

We define Hamiltonian simplex differential graded algebras (DGA) with differentials that deform the high-energy symplectic homology differential and wrapped Floer homology differential in the cases of closed and open strings in a Liouville manifold of finite type, respectively. The order-m term in the differential is induced by varying natural degree-m coproducts over an (m1)–simplex, where the operations near the boundary of the simplex are trivial. We show that the Hamiltonian simplex DGA is quasi-isomorphic to the (nonequivariant) contact homology algebra and to the Legendrian homology algebra of the ideal boundary in the closed and open string cases, respectively.

Keywords
symplectic homology, wrapped Floer homology, contact homology, symplectic field theory
Mathematical Subject Classification 2010
Primary: 53D40, 53D42
Secondary: 16E45, 18G55
References
Publication
Received: 20 August 2015
Revised: 16 June 2016
Accepted: 24 August 2016
Published: 19 May 2017
Proposed: Yasha Eliashberg
Seconded: András I. Stipsicz, Ciprian Manolescu
Authors
Tobias Ekholm
Department of Mathematics
University of Uppsala
Box 480
SE-751 06 Uppsala
Sweden
Alexandru Oancea
Sorbonne Universités, UPMC Univ. Paris 06
UMR 7586, Institut de Mathématiques de Jussieu-Paris Rive Gauche
Case 247
4 place Jussieu
75005 Paris
France