#### Volume 21, issue 4 (2017)

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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 $\left(m-1\right)$–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