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Proceedings of the American Mathematical Society

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



Spaces dominated by two-complexes

Author: Sushil Jajodia
Journal: Proc. Amer. Math. Soc. 82 (1981), 288-290
MSC: Primary 57M20
MathSciNet review: 609669
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Abstract: We say a group $ G$ is of geometric dimension $ \leqslant 2$ if there is an aspherical $ 2$-dimensional CW-complex $ P$ with fundamental group isomorphic to $ G$. In this note, we study the following problem: Suppose $ G$ is a group of geometric dimension $ \leqslant 2$ with associated aspherical $ 2$-dimensional CW-complex $ P$. Suppose further that $ X$ is a CW-complex having fundamental group isomorphic to $ G$ and that $ X$ is dominated by a $ 2$-complex. If the Wall invariant $ {\text{W}}{{\text{a}}_2}[X] \in {\tilde K_0}(ZG)$ vanishes, does $ X$ have the same homotopy type as $ P \vee k{S^2}$ where $ k{S^2}$ denotes the sum of $ k$ copies of the $ 2$-sphere $ {S^2}$?

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Article copyright: © Copyright 1981 American Mathematical Society

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