Virtual 1-domination of 3-manifolds
- 27 February 2018
- journal article
- research article
- Published by Cambridge University Press (CUP) in Compositio Mathematica
- Vol. 154 (3) , 621-639
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
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This publication has 11 references indexed in Scilit:
- Strict contractions and exotic SO0(d,1) quotientsJournal of the London Mathematical Society, 2017
- Homology of curves and surfaces in closed hyperbolic 3-manifoldsDuke Mathematical Journal, 2015
- Virtual domination of 3–manifoldsGeometry & Topology, 2015
- Virtual homological torsion of closed hyperbolic 3-manifoldsJournal of Differential Geometry, 2015
- Incompressible Surfaces in Rank One Locally Symmetric SpacesGeometric and Functional Analysis, 2015
- Complex Fenchel-Nielsen coordinates with small imaginary partsTransactions of the American Mathematical Society, 2014
- From Riches to Raags: 3-Manifolds, Right-Angled Artin Groups, and Cubical Geometry2012
- Immersing almost geodesic surfaces in a closed hyperbolic three manifoldAnnals of Mathematics, 2012
- Non-zero degree maps and surface bundles over $S\sp 1$Journal of Differential Geometry, 1996
- Subgroups of Surface Groups are Almost GeometricJournal of the London Mathematical Society, 1978