Homotopy groups of highly connected manifolds

2015/10/18 by Basu, Samik, Basu, Somnath · 1 citation
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.05195

Abstract

In this paper we give a formula for the homotopy groups of (n-1)-connected 2n-manifolds as a direct sum of homotopy groups of spheres in the case the n^th Betti number is larger than 1. We demonstrate that when the n^th Betti number is 1 the homotopy groups might not have such a decomposition. The techniques used in this computation also yield formulae for homotopy groups of connected sums of sphere products and CW complexes of a similar type. In all the families of spaces considered here, we establish a conjecture of J. C. Moore.

Cited by

• Anick's conjecture for polyhedral products

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