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 P = (x, r) is an aspherical presentation of the trivial group, and r 0 ∈ r a fixed relation, then P 1 = (x, r 1 ) is aspherical where r 1 = r \ {r 0 }.

Whitehead aspherical conjecture via ribbon sphere-link

“…The author found on the Internet the preprint of E. Pasku [12] reporting the same result which appears obtained by a purely group theoretic argument, much different from the present argument.…”

Whitehead Aspherical Conjecture via Ribbon Sphere-Link

“…The author mentions here that there is a preprint by Pasku claiming the same result, which is a purely group-theoretic argument much different from the current argument [5].…”