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

IF 1.6 2区数学 Q2 MATHEMATICS

Journal of Topology Pub Date : 2026-02-25 DOI:10.1112/topo.70066

Lea Kenigsberg, Noah Porcelli

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引用次数: 0

Abstract

Given $f : M \to N$ a homotopy equivalence of compact manifolds with boundary, we use a construction of Geoghegan and Nicas to define its Reidemeister trace $[T] \in π_{1}^{s t} (L N, N)$ . We realize the Goresky–Hingston coproduct as a map of spectra, and show that the failure of $f$ to entwine the spectral coproducts can be characterized by Chas–Sullivan multiplication with $[T]$ . In particular, when $f$ is a simple homotopy equivalence, the spectral coproducts of $M$ and $N$ agree.

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参数化不动点理论对环副积同伦不变性的阻碍

给定f：M→N $f:M \rightarrow N$有边界紧流形的同伦等价，我们使用Geoghegan和Nicas的构造来定义它的Reidemeister迹[T]∈π 1 s T (L N， N) $[T] \in \pi _1^{st}(\mathcal {L}N, N)$。我们认识到Goresky-Hingston副积是光谱的映射，并表明f $f$不能缠绕谱副积可以用与[T] $[T]$的Chas-Sullivan乘法来表征。特别地，当f $f$是一个简单同伦等价时，M $M$和N $N$的谱余积一致。

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来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.