On L^2-Betti numbers of Gromov-Thurston branched covers
Grigori Avramidi (Max Planck Institute for Mathematics)
Monday 20th January 16:00-17:00 Maths 311B
Abstract
Gromov and Thurston constructed infinite families of manifolds that have metrics of pinched negative curvature but no metrics of constant negative curvature by taking cyclic branched covers of hyperbolic manifolds over codimension-two, totally geodesic submanifolds. We show that some of these branched covers satisfy Singer's L^2-Betti number vanishing conjecture using skew fields and special cube complex technology, partially answering a question raised by Gromov. Joint work with Boris Okun and Kevin Schreve.
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