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 nth Betti number is larger than 1. We demonstrate that when the nth Betti number is 1 the homotopy groups might not have such a decomposition. The techniques used in this computation also yield formulas 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.
Publication Year: 2006
Publication Date: 2006-10-01
Language: en
Type: letter
Indexed In: ['crossref', 'pubmed']
Access and Citation
Cited By Count: 18
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot