## Geometry & Topology

### Symplectic and contact differential graded algebras

#### 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 $(m−1)$–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.

#### Article information

Source
Geom. Topol., Volume 21, Number 4 (2017), 2161-2230.

Dates
Revised: 16 June 2016
Accepted: 24 August 2016
First available in Project Euclid: 19 October 2017

https://projecteuclid.org/euclid.gt/1508437639

Digital Object Identifier
doi:10.2140/gt.2017.21.2161

Mathematical Reviews number (MathSciNet)
MR3654106

Zentralblatt MATH identifier
06726519

#### Citation

Ekholm, Tobias; Oancea, Alexandru. Symplectic and contact differential graded algebras. Geom. Topol. 21 (2017), no. 4, 2161--2230. doi:10.2140/gt.2017.21.2161. https://projecteuclid.org/euclid.gt/1508437639

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