Ivanov's asphericity conjecture

Let

P=[x1,x2,,xnr1,r2,,rm]\mathcal{P}=[ x_1,x_2,\ldots,x_n\mid r_1,r_2,\ldots,r_m]

be an aspherical presentation. Let

Q=[x1,x2,,xn,xr1,r2,,rm,r]\mathcal{Q}=[ x_1,x_2,\ldots,x_n,x\mid r_1,r_2,\ldots,r_m,r]

be a presentation such that the total exponent of xx in rr is nonzero, the group HH presented by P\mathcal{P} naturally embeds in the group GG presented by Q\mathcal{Q}, and GG is torsion-free.

Ivanov's asphericity conjecture. Then Q\mathcal{Q} is aspherical.

The conjecture is refuted: Ivanov showed that a counterexample would provide a torsion-free group whose integral group ring contains zero divisors, while the supplied status evidence records the conjecture as disproved.

Sources & referencesView supporting material

Primary source

Jonathan Ariel Barmak and Elias Gabriel Minian, “A new test for asphericity and diagrammatic reducibility of group presentations”, arXiv:1601.00604 (2016).

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