Geometry & Topology

Symplectic and contact differential graded algebras

Tobias Ekholm and Alexandru Oancea

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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-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.

Article information

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

Received: 20 August 2015
Revised: 16 June 2016
Accepted: 24 August 2016
First available in Project Euclid: 19 October 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53D40: Floer homology and cohomology, symplectic aspects 53D42: Symplectic field theory; contact homology
Secondary: 16E45: Differential graded algebras and applications 18G55: Homotopical algebra

symplectic homology wrapped Floer homology contact homology symplectic field theory


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.

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