Reduced symplectic homology and string topology
arXiv:2209.02972 · doi:10.2140/tunis.2026.8.203
Abstract
We introduce a common domain of definition for the loop product and the loop coproduct, reduced loop homology, on which they combine to a unital infinitesimal anti-symmetric bialgebra structure. In particular, a relation conjectured by Sullivan holds with an extra term. The structure depends on choices governed by secondary continuation maps. These results on string topology are proved in the more general context of reduced symplectic homology for a suitable class of Weinstein manifolds.
70 pages, 11 figures. Title changed to put emphasis on applications to string topology. Details added in several proofs, improved exposition. This is the final version of the paper, to be published in Tunisian Journal of Mathematics
References in corpus (11)
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- Topological quantum field theory structure on symplectic cohomology
- Duality between Lagrangian and Legendrian invariants
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- Symplectic and contact differential graded algebras
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- Homotopically trivializing the circle in the framed little disks