Abstract
Let be a closed manifold that admits a self-cover of degree . We say is strongly regular if all iterates are regular covers. In this case, we establish an algebraic structure theorem for the fundamental group of : We prove that surjects onto a nontrivial free abelian group , and the self-cover is induced by a linear endomorphism of . Under further hypotheses we show that a finite cover of admits the structure of a principal torus bundle. We show that this applies when is Kähler and is a strongly regular, holomorphic self-cover, and prove that a finite cover of splits as a product with a torus factor.
Citation
Wouter van Limbeek. "Towers of regular self-covers and linear endomorphisms of tori." Geom. Topol. 22 (4) 2427 - 2464, 2018. https://doi.org/10.2140/gt.2018.22.2427
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