Homotopy groups of highly connected Poincaré duality complexes
Piotr Beben, Stephen Theriault
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 Poincaré Duality complexes of dimension 2n or 2n+1 with minor cohomological conditions.
Topics & Concepts
MathematicsPoincaré dualityHomotopyDuality (order theory)Pure mathematicsPoincaré conjectureHomotopy groupCohomologyHomotopy and Cohomology in Algebraic TopologyAdvanced Topics in AlgebraAlgebraic structures and combinatorial models