Two results on asphericity

Roman Mikhailov

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arXiv · 2608.20270

Two results on asphericity

Roman Mikhailov

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Abstract

We construct an explicit finite chain of non-aspherical group presentation complexes $K(\mathcal X)\subset K(\mathcal Y)\subset K(\mathcal Z)$ in which $K(\mathcal Y)$ is Cockcroft, both inclusion-induced maps on $\pi_2$ are zero, and the pair $(K(\mathcal Y),K(\mathcal X))$ has the identity property. This answers a question of Hitchman. The construction is given directly from a short balanced presentation of the binary icosahedral group. As the second result, we construct an integral Lie ring presentation in which a subpresentation has a nontrivial identity among relations, whereas the presentation itself has none.

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Roman Mikhailov. 2026-08-20. Two results on asphericity. https://arxiv.org/abs/2608.20270

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