Speaker: Prof. Stephen Theriault，University of Southampton

Inviter: 黄瑞芝副研究员

Title: Properties of Poincare Duality complexes - from rational to integral

Language: English

Time & Venue: 2025.04.02 14:30-15:30 南楼N818

Abstract: A provocative theorem of Halperin and Lemaire states that if M is a simply-connected Poincare Duality complex of dimension n and the rational cohomology of M is not generated as an algebra by a single element, then the based loops on M retracts off the based loops on its (n-1)-skeleton. This implies that the attaching map for the n-cell of M kills off homotopy groups but does not introduce any new ones. It is rare that a cell attachment has this property and it is surprising that it holds in such generality for Poincare Duality complexes.In this talk we show that this theorem secretly originates in integral homotopy theory. We give conditions for when the based loops on M integrally retracts off the based loops on its (n-1)-skeleton, and use these to recover the rational result.