Towers of regular self-covers and linear endomorphisms of tori

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• Wouter Van Limbeek (University of Michigan)
• Monday 08 May 2017, 13:30-14:30
• Seminar Room 1, Newton Institute.

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NPCW04 - Approximation, deformation, quasification

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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