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On the second homotopy module of two-dimensional CW complexes


Author: M. N. Dyer
Journal: Proc. Amer. Math. Soc. 55 (1976), 400-404
MSC: Primary 55E05
DOI: https://doi.org/10.1090/S0002-9939-1976-0410739-6
MathSciNet review: 0410739
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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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DOI: https://doi.org/10.1090/S0002-9939-1976-0410739-6
Article copyright: © Copyright 1976 American Mathematical Society

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