Spaces dominated by two-complexes
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- by Sushil Jajodia PDF
- Proc. Amer. Math. Soc. 82 (1981), 288-290 Request permission
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 ${S^2}$?References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 82 (1981), 288-290
- MSC: Primary 57M20
- DOI: https://doi.org/10.1090/S0002-9939-1981-0609669-8
- MathSciNet review: 609669