Symplectic and contact differential graded algebras

Ekholm, Tobias¹ ; Oancea, Alexandru²

¹ Department of Mathematics, University of Uppsala, Box 480, SE-751 06 Uppsala, Sweden
² Sorbonne Universités, UPMC Univ. Paris 06, UMR 7586, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Case 247, 4 place Jussieu, 75005 Paris, France

Geometry & topology, Tome 21 (2017) no. 4, pp. 2161-2230.

Résumé

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 $\left(m-1\right)$–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.

Détail

DOI : 10.2140/gt.2017.21.2161

Classification : 53D40, 53D42, 16E45, 18G55
Keywords: symplectic homology, wrapped Floer homology, contact homology, symplectic field theory

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