On the second homotopy module of two-dimensional CW complexes

Dyer, M. N.

doi:10.1090/S0002-9939-1976-0410739-6

On the second homotopy module of two-dimensional CW complexes
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by M. N. Dyer

Proc. Amer. Math. Soc. 55 (1976), 400-404

DOI: https://doi.org/10.1090/S0002-9939-1976-0410739-6

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Abstract:

Let $X$ be a connected $2$-dimensional ${\text {CW}}$ complex. This note reproves from a very simple point of view two classical theorems of H. Hopf relating the homology of the fundamental group $\pi = {\pi _1}(X)$ of $X$ and the Hurewicz map on ${\pi _2}(X)$. This point of view also allows the dual theorems to be proved. If $\pi$ is a finite group, a new interpretation is given for ${H_i}(\pi ;Z)(i = 2,3)$ in terms of ${\pi _2}(X)$.

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The homotopy theory of

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