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Virtual 1-domination of 3-manifolds

Part of: Low-dimensional topology

Published online by Cambridge University Press:  27 February 2018

Yi Liu  and
Hongbin Sun
Yi Liu
Affiliation:
Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China email [email protected]
Hongbin Sun
Affiliation:
Department of Mathematics, UC Berkeley, CA 94720, USA email [email protected]
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Abstract

It is shown in this paper that given any closed oriented hyperbolic 3-manifold, every closed oriented 3-manifold is mapped onto by a finite cover of that manifold via a map of degree 1, or in other words, virtually 1-dominated by that manifold. This improves a known result of virtual 2-domination. The proof invokes a recently developed enhanced version of the connection principle in good pants constructions.

Keywords

good pantsnon-zero degree mapvirtual property

MSC classification

Primary: 57M10: Covering spaces 57M50: Geometric structures on low-dimensional manifolds
Type
Research Article
Information
Compositio Mathematica , Volume 154 , Issue 3 , March 2018 , pp. 621 - 639
Copyright
© The Authors 2018 

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