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arXiv · 1812.07559

Finiteness of homotopy groups related to the non-abelian tensor product

Raimundo Bastos·Noraí R. Rocco·Ewerton R. Vieira
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Abstract

By using finiteness related result of non-abelian tensor product we prove finiteness conditions for the homotopy groups $\pi_n(X)$ in terms of the number of tensors. In particular, we establish a quantitative version of the classical Blakers-Massey triad connectivity theorem. Moreover, we study others finiteness conditions and equivalence properties that arise from the non-abelian tensor square. In the end, we give applications to homotopy pushout, especially in the case of Eilenberg-MacLane spaces.

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Raimundo Bastos, Noraí R. Rocco, Ewerton R. Vieira. 2018-12-18. Finiteness of homotopy groups related to the non-abelian tensor product. https://doi.org/10.1007/s10231-019-00855-8

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