Volume 21, issue 4 (2017)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 6, 2483–2999
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
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