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Chain-Level String Topology Operations

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arxiv 1506.02596 v1 pith:FS4APOCU submitted 2015-06-08 math.GT math.AT

Gabriel C. Drummond-Cole , Kate Poirier , Nathaniel Rounds This is my paper · ORCID
classification math.GTmath.AT
keywords spacestringoperationschainsdiagramsfreelooptopology
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We construct a space of string diagrams, which are a type of fatgraph with some additional data, and show that there are string topology operations on the chains of the free loop space of a closed Riemannian manifold which are parameterized by the chains on the space of string diagrams. These operations are shown to recover known structure on homology of the free loop space.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the invariance of the string topology coproduct

    math.AT 2019-08 reject novelty 7.0 of 10

    A proposed proof of homotopy invariance of the string topology coproduct fails because a key map does not fix the required boundary subspaces.

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