Stable splitting of mapping spaces via nonabelian Poincaré duality

2017/05/08 by Lauren Bandklayder, Bandklayder, Lauren · 1 citation
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1705.03090

openalex publication_date 2017/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use nonabelian Poincaré duality to recover the stable splitting of compactly supported mapping spaces, \rmMap_c(M,ΣⁿX), where M is a parallelizable n-manifold. Our method for deriving this splitting is new, and naturally extends to give a more general stable splitting of the space of compactly supported sections of a certain bundle on M with fibers ΣⁿX, twisted by the tangent bundle of M. This generalization incorporates possible O(n)-actions on X as well as accommodating non-parallelizable manifolds.

Cited by

• Configuration spaces in algebraic topology

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