On the invariance of the string topology coproduct

2019/08/11 by Nathalie Wahl, Wahl, Nathalie · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algebraic Topology (math.AT) #Algorithms and Data Compression #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1908.03857

openalex publication_date 2019/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a variant of Naef's formula for the failure of invariance of the string topology coproduct under homotopy equivalences, using an obstruction class built from homotopy data associated to a homotopy equivalence as well as the ``fake diagonal''. The vanishing of our obstruction class can be seen as a way to measure a form of boundedness for homotopy equivalences. We show that the same obstruction rules the failure of invariance for a generalization of the coproduct to higher dimensional loops.

Citations

• String topology and configuration spaces of two points
• Obstructions to homotopy invariance of loop coproduct via parametrised fixed-point theory

Cited by

• The Goresky-Hingston Coproduct on Based Loop Spaces

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• Intersection Multiplicity in Loop Spaces and the String Topology Coproduct
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