An answer to the Whitehead asphericity question

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 ${\mathbf{r}}_1=\mathbf{r}\setminus \{r_0\}$.

41 pages. arXiv admin note: text overlap with arXiv:1407.6283