A Higman embedding preserving asphericity

Sapir, Mark¹

¹ Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240

Journal of the American Mathematical Society, Tome 27 (2014) no. 1, pp. 1-42

Résumé

We prove that every finitely generated group with recursive aspherical presentation embeds into a group with finite aspherical presentation. This and several known facts about groups and manifolds imply that there exists a 4-dimensional closed aspherical manifold $M$ such that the fundamental group $\pi _1(M)$ coarsely contains an expander. Thus it has infinite asymptotic dimension, is not coarsely embeddable into a Hilbert space, does not satisfy G. Yu’s property A, and does not satisfy the Baum-Connes conjecture with coefficients. Closed aspherical manifolds with any of these properties were previously unknown.

Détail

DOI : 10.1090/S0894-0347-2013-00776-6

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