A proposed proof of homotopy invariance of the string topology coproduct fails because a key map does not fix the required boundary subspaces.
Chain-Level String Topology Operations
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abstract
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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On the invariance of the string topology coproduct
A proposed proof of homotopy invariance of the string topology coproduct fails because a key map does not fix the required boundary subspaces.