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arXiv · 1806.04475

An upper bound on the LS-category in presence of the fundamental group

Alexander Dranishnikov
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Abstract

We prove that $$ \cat X\le \frac{\cd(\pi_1(X))+\dim X}{2}$$ for every CW complex $X$ where $\cd(\pi_1(X))$ denotes the cohomological dimension of the fundamental group of $X$. We obtain this as a corollary of the inequality $$ \cat X\le\frac{\cat (u_X)+\dim X}{2} $$ where $u_X:X\to B\pi_1(X)$ is a classifying map for the universal covering of $X$.

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Alexander Dranishnikov. 2018-06-12. An upper bound on the LS-category in presence of the fundamental group. https://doi.org/10.2140/agt.2019.19.3601

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