A combinatorial description of homotopy groups of spheres

Abstract

We give a combinatorial description of general homotopy groups of $k$-dimensional spheres with $k\ge 3$ as well as those of Moore spaces. For $n>k\ge 3,$ we construct a finitely generated group defined by explicit generators and relations, whose center is exactly ${\pi }_n(S^k)$.

27 pages, 1 figure

References in corpus (1)

• Brunnian Braids on Surfaces

Cited by in corpus (1)

• Homotopy groups as centers of finitely presented groups