The Homotopy Type of a Poincaré Duality Complex after Looping

2011/02/08 by Beben, Piotr, Wu, Jie
#55P15 #55P35 #57N65 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1102.1516

Abstract

We answer a weaker version of the classification problem for the homotopy types of (n-2)-connected closed orientable (2n-1)-manifolds. Let n≥ 6 be an even integer, and X be a (n-2)-connected finite orientable Poincaré (2n-1)-complex such that H^n-1(X;ℚ)=0 and H^n-1(X;ℤ₂)=0. Then its loop space homotopy type is uniquely determined by the action of higher Bockstein operations on H^n-1(X;ℤ_p) for each odd prime p. A stronger result is obtained when localized at odd primes.

Related

• Suspension Homotopy of (n-1)-connected (2n+2)-dimensional Poincaré Duality Complexes
• Homotopy groups of highly connected Poincare duality complexes
• Loop spaces of n-dimensional Poincaré duality complexes whose (n-1)-skeleton is a co-H-space
• Manifold structures on highly connected Poincaré complexes
• The homotopy type of the loops on (n-1)-connected (2n+1)-manifolds