Homotopy of manifolds stabilized by projective spaces

2022/04/09 by Ruizhi Huang, Huang, Ruizhi, Stephen Theriault +1 · 1 citation
Mathematics · Medicine · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders

paper · pdf · doi:10.48550/arxiv.2204.04368

openalex publication_date 2022/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the homotopy of the connected sum of a manifold with a projective space, viewed as a typical way to stabilize manifolds. In particular, we show a loop homotopy decomposition of a manifold after stabilization by a projective space, and provide concrete examples. To do this, we trace the effect in homotopy theory of surgery on certain product manifolds by showing a loop homotopy decomposition after localization away from the order of the image of the classical J-homomorphism.

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