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- 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.
Citation
Tobias Ekholm. Alexandru Oancea. "Symplectic and contact differential graded algebras." Geom. Topol. 21 (4) 2161 - 2230, 2017. https://doi.org/10.2140/gt.2017.21.2161
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