2021/10/15 by Inbar Klang, Klang, Inbar, Sarah Yeakel +1 · 2 citations
Computer Science · Mathematics · Medicine · #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2110.07853
openalex publication_date 2021/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An isovariant map is an equivariant map between G-spaces which strictly preserves isotropy groups. We consider an isovariant analogue of Klein--Williams equivariant intersection theory for a finite group G. We prove that under certain reasonable dimension and codimension conditions on H-fixed subspaces (for H≤ G), the fixed points of a self-map of a compact smooth G-manifold can be removed isovariantly if and only if the equivariant Reidemeister trace of the map vanishes. In doing so, we study isovariant maps between manifolds up to isovariant homotopy, yielding an isovariant Whitehead's theorem. In addition, we speculate on the role of isovariant homotopy theory in distinguishing manifolds up to homeomorphism.