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Towers of regular self-covers and linear endomorphisms of tori

Presented by: 
Wouter Van Limbeek University of Michigan
Date: 
Monday 8th May 2017 - 13:30 to 14:30
Venue: 
INI Seminar Room 1
Abstract: 
Let M be a closed manifold that admits a nontrivial cover diffeomorphic to itself. What can we then say about M? Examples are provided by tori, in which case the covering is homotopic to a linear endomorphism. Under the assumption that all iterates of the covering of M are regular, we show that any self-cover is is induced by a linear endomorphism of a torus on a quotient of the fundamental group. Under further hypotheses we show that a finite cover of M is a principal torus bundle. We use this to give an application to holomorphic self-covers of Kaehler manifolds.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons