Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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)$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55E05

Retrieve articles in all journals with MSC: 55E05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0410739-6
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society