Ivanov's asphericity conjecture

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Let

P=[x1,x2,…,xn∣r1,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,x∣r1,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.

References

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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