Homotopy groups of highly connected manifolds

Article Type

Research Article

Publication Title

Advances in Mathematics

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.

First Page

363

Last Page

416

DOI

10.1016/j.aim.2018.08.006

Publication Date

10-15-2018

Comments

All Open Access, Green

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