Two results on asphericity
Roman Mikhailov
Abstract
We construct an explicit finite chain of non-aspherical group presentation complexes K( X)⊂ K( Y)⊂ K( Z) in which K( Y) is Cockcroft, both inclusion-induced maps on π2 are zero, and the pair (K( Y),K( 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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