Homotopy groups of highly connected Poincare duality complexes

2018/12/13 by Piotr Beben, Beben, Piotr, Stephen Theriault +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1812.05344

openalex publication_date 2018/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Methods are developed to relate the action of a principal fibration to relative Whitehead products in order to determine the homotopy type of certain spaces. The methods are applied to thoroughly analyze the homotopy type of the based loops on certain cell attachments. Key examples are (n-1)-connected Poincare Duality complexes of dimension 2n or 2n+1 with minor cohomological conditions.

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