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Symplectic and contact differential graded algebras. (English) Zbl 1473.53097

Summary: 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.

MSC:

53D40 Symplectic aspects of Floer homology and cohomology
53D42 Symplectic field theory; contact homology
16E45 Differential graded algebras and applications (associative algebraic aspects)
18G99 Homological algebra in category theory, derived categories and functors
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