Homology of curves and surfaces in closed hyperbolic 3-manifolds

Author: 

Liu, Y
Markovic, V

Publication Date: 

1 January 2015

Journal: 

Duke Mathematical Journal

Last Updated: 

2021-01-10T14:19:07.76+00:00

Issue: 

14

Volume: 

164

DOI: 

10.1215/00127094-3167744

page: 

2723-2808

abstract: 

© 2015. Among other things, we prove the following two topological statements about closed hyperbolic 3-manifolds. First, every rational second homology class of a closed hyperbolic 3-manifold has a positive integral multiple represented by an oriented connected closed π1-injectively immersed quasi-Fuchsian subsurface. Second, every rationally null-homologous, π1-injectively immersed oriented closed 1-submanifold in a closed hyperbolic 3-manifold has an equidegree finite cover which bounds an oriented connected compact π1-injectively immersed quasi-Fuchsian subsurface. In, we exploit techniques developed by Kahn and Markovic but we only distill geometric and topological ingredients from those papers, so no hard analysis is involved in this article.

Symplectic id: 

1109988

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article