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Abstract
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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-
term in the differential is induced by varying natural
degree- coproducts
over an
–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.
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Keywords
symplectic homology, wrapped Floer homology, contact
homology, symplectic field theory
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Mathematical Subject Classification 2010
Primary: 53D40, 53D42
Secondary: 16E45, 18G55
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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
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