Homotopy groups of highly connected manifolds

Authors

Samik Basu, Indian Statistical Institute, Kolkata
Somnath Basu, Indian Institute of Science Education and Research Kolkata

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

Recommended Citation

Basu, Samik and Basu, Somnath, "Homotopy groups of highly connected manifolds" (2018). Journal Articles. 1191.
https://digitalcommons.isical.ac.in/journal-articles/1191