Homotopy groups of highly connected Poincaré duality complexes

  • Piotr Beben

    International TechneGroup Ltd, Cambridge CB24 4UQ, United Kingdom
  • Stephen Theriault

    Mathematical Sciences, University of Southampton, Southampton SO17 1BJ, United Kingdom
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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 (n1)(n-1)-connected Poincaré Duality complexes of dimension 2n2n or 2n+12n+1 with minor cohomological conditions.

Cite this article

Piotr Beben, Stephen Theriault, Homotopy groups of highly connected Poincaré duality complexes. Doc. Math. 27 (2022), pp. 183–211

DOI 10.4171/DM/869