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A parametrized Pontryagin--Thom theorem

2025/12/11 by David Ayala, Ayala, David, John Francis +1
Mathematics · #55U10 #58D29 #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Primary 57R90. Secondary 57N75

paper · pdf · doi:10.48550/arxiv.2512.10274

openalex publication_date 2025/12/11 · openalex created_date 2025/12/13 · openalex updated_date 2026/07/28

Abstract

We prove a space-level enhancement of the Pontryagin--Thom theorem, identifying the space of maps from a manifold to a Thom space with a moduli space of submanifolds.

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