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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
DOI: https://doi.org/10.1090/S0002-9947-1980-0567093-4
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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Article copyright: © Copyright 1980 American Mathematical Society