Geometry & Topology
- Geom. Topol.
- Volume 21, Number 4 (2017), 2161-2230.
Symplectic and contact differential graded algebras
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.
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
Permanent link to this document
Digital Object Identifier
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
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