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

Dyer, Micheal N.

doi:10.1090/S0002-9947-1980-0567093-4

An application of homological algebra to the homotopy classification of two-dimensional CW-complexes
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by Micheal N. Dyer

Trans. Amer. Math. Soc. 259 (1980), 505-514

DOI: https://doi.org/10.1090/S0002-9947-1980-0567093-4

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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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