A bordism approach to string topology

By D. Chataur. 2003

49 citations recorded by the source corpus.

Using intersection theory in the context of Hilbert manifolds and geometric homology we show how to recover the main operations of string topology built by M. Chas and D. Sullivan. We also study and build an action of the homology of reduced Sullivan's chord diagrams on the singular homology of free loop spaces, extending previous results of R. Cohen and V. Godin and unifying part of the rich algebraic structure of string topology as an algebra over the prop of these reduced diagrams. Some of these operations are extended to spaces of maps from a sphere to a compact manifold.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5aab6f50d0efe8586d70dae9b80de27ba7c713bf

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In Geometry and Topology

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Citations in the corpus

Moduli space actions on the Hochschild co-chains of a Frobenius algebra I: cell operads (2006, background): “The second source is the string topology of Chas and Sullivan [CS, V2, CJ, C, CG, Ch , Me, S1, S2], and lastly the third source are considerations of D-branes in open/closed string theory as deformations of the Hochschild complex see e.g.”
Hochschild homology of structured algebras (2011, unknown): “One has to be aware that authors sometimes restrict to non-degenerate diagrams, those such that collapsing the chords does not change the homotopy type of the graph (as in for example [8, 9, 27]).”
Loop Products and Closed Geodesics (2007, background): “cross product. The map τ is the Thom isomorphism (B.1.2) for the normal bundle νF of F = � ×M � in � × � ([ Cht ] Prop.”