Work

Obstructions to homotopy invariance of loop coproduct via parameterized fixed‐point theory

Year: 2026

Type: article

Abstract: Given a homotopy equivalence of compact manifolds with boundary, we use a construction of Geoghegan and Nicas to define its Reidemeister trace . We realize the Goresky–Hingston coproduct as a map of spectra, and show that the failure of to entwine the spectral coproducts can be characterized by Chas–Sullivan multiplication with . In particular, when is a simple homotopy equivalence, the spectral coproducts of and agree.

Source: Journal of Topology

DOI: 10.1112/topo.70066

Authors: Lea Kenigsberg, Noah Porcelli

Institutions: University of California, Davis, Max Planck Institute for Mathematics

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funder: Engineering and Physical Sciences Research Council