A combinatorial description of homotopy groups of spheres

Roman Mikhailov; Jie Wu

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arXiv · 1108.3055

A combinatorial description of homotopy groups of spheres

Roman Mikhailov·Jie Wu

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Abstract

We give a combinatorial description of general homotopy groups of $k$-dimensional spheres with $k\geq3$ as well as those of Moore spaces. For $n>k\geq 3,$ we construct a finitely generated group defined by explicit generators and relations, whose center is exactly $\pi_n(S^k)$.

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Roman Mikhailov, Jie Wu. 2011-08-15. A combinatorial description of homotopy groups of spheres. https://arxiv.org/abs/1108.3055

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