Virtual 1-domination of 3-manifolds. (27th February 2018)

• Record Type: Journal Article
• Authors: Liu, Yi; Sun, Hongbin
• Is Part Of: Compositio mathematica. Volume 154:Number 3(2018)
• Page Start: 621
• Page End: 639
• Publication Date: 2018-02-27
• Subjects: 57M10, -- 57M50 (primary); good pants, -- non-zero degree map, -- virtual property; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X17007965
• Languages: English
• ISSNs: 0010-437X

Abstract

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.