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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

An application of homological algebra to the homotopy classification of two-dimensional CW-complexes


Author: Micheal N. Dyer
Journal: Trans. Amer. Math. Soc. 259 (1980), 505-514
MSC: Primary 55P15; Secondary 57M05, 57M20
MathSciNet review: 567093
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Abstract: Let $ \pi $ be $ {Z_m}\, \times \,{Z_n}$. In this paper the homotopy types of finite connected two dimensional CW-complexes with fundamental group $ \pi $ are shown to depend only on the Euler characteristic. The basic method is to study the structure of the group $ {\text{Ext}}_{Z\pi }^1(I{\pi ^2},\,Z)$ as a principal $ {\text{End(}}I{\pi ^2}{\text{)}}$-module.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1980-0567093-4
PII: S 0002-9947(1980)0567093-4
Article copyright: © Copyright 1980 American Mathematical Society