Monday, 1 August, 11:00-12:00, Room 4102


Mark Sapir (Vanderbilt University)


Aspherical groups and manifolds with extreme properties


I prove that every finitely generated group with recursive
aspherical presentation complex embeds into a group with finite
aspherical presentation complex. Using Gromov's random groups and the
Davis' trick, this implies existence of aspherical manifolds whose
fundamental groups do not coarsely embed into Hilbert spaces, do not
satisfy property A, have infinite asymptotic dimension and do not
satisfy the Baum-Connes conjecture with coefficients.

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