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arXiv · 2107.12293

An answer to the Whitehead asphericity question

Elton Pasku
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Abstract

The Whitehead asphericity problem, regarded as a problem of combinatorial group theory, asks whether any subpresentation of an aspherical group presentation is also aspherical. We give a positive answer to this question by proving that if $\cP=(\mathbf{x}, \mathbf{r})$ is an aspherical presentation of the trivial group, and $r_{0} \in \mathbf{r}$ a fixed relation, then $\cP_{1}=(\mathbf{x}, \mathbf{r}_{1})$ is aspherical where $\mathbf{r}_{1}=\mathbf{r} \setminus \{r_{0}\}$.

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Elton Pasku. 2021-07-26. An answer to the Whitehead asphericity question. https://arxiv.org/abs/2107.12293

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