The Loop Space Homotopy Type of Simply-connected Four-manifolds and their Generalizations

2014/06/03 by Beben, Piotr, Theriault, Stephen · 2 citations
#55P35 #57N65 #57P10 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1406.0651

Abstract

We determine loop space decompositions of simply-connected four-manifolds, (n-1)-connected 2n-dimensional manifolds provided n∉\4,8\, and connected sums of products of two spheres. These are obtained as special cases of a more general loop space decomposition of certain torsion-free CW-complexes with well-behaved skeleta and some Poincaré duality features.

Cited by

• Anick's conjecture for polyhedral products
• Homotopy types of moment-angle complexes associated to almost linear resolutions

Related

• The Free Loop Space Homology of (n-1)-connected 2n-manifolds
• Loop spaces of n-dimensional Poincaré duality complexes whose (n-1)-skeleton is a co-H-space
• The homotopy type of the loops on (n-1)-connected (2n+1)-manifolds
• Loop Space Decompositions of Connected Sums and Applications to the Vigué-Poirrier Conjecture
• Sphere bundles over 4-manifolds are trivial after looping