Homotopy groups of highly connected Poincaré duality complexes

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) -connec...

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Bibliographic Details
Published inDocumenta mathematica Journal der Deutschen Mathematiker-Vereinigung. Vol. 27; pp. 183 - 211
Main Authors Beben, Piotr, Theriault, Stephen
Format Journal Article
LanguageEnglish
Published 2022
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Summary: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 Poincaré Duality complexes of dimension 2n or 2n+1 with minor cohomological conditions.
ISSN:1431-0635
1431-0643
DOI:10.4171/dm/869