The homotopy type of the loops on (n-1)-connected (2n+1)-manifolds

2018/10/16 by Samik Basu, Basu, Samik
Computer Science · Mathematics · #55Q52 #57N15 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary : 55P35 #Secondary : 16S37 #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1810.07549

openalex publication_date 2018/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For n≥ 2 we compute the homotopy groups of (n-1)-connected closed manifolds of dimension (2n+1). Away from the finite set of primes dividing the order of the torsion subgroup in homology, the p-local homotopy groups of M are determined by the rank of the free Abelian part of the homology. Moreover, we show that these p-local homotopy groups can be expressed as a direct sum of p-local homotopy groups of spheres. The integral homotopy type of the loop space is also computed and shown to depend only on the rank of the free Abelian part and the torsion subgroup.

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