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1 November 2015 Homology of curves and surfaces in closed hyperbolic 3-manifolds
Yi Liu, Vladimir Markovic
Duke Math. J. 164(14): 2723-2808 (1 November 2015). DOI: 10.1215/00127094-3167744

Abstract

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.

Citation

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Yi Liu. Vladimir Markovic. "Homology of curves and surfaces in closed hyperbolic 3-manifolds." Duke Math. J. 164 (14) 2723 - 2808, 1 November 2015. https://doi.org/10.1215/00127094-3167744

Information

Received: 12 November 2013; Revised: 7 December 2014; Published: 1 November 2015
First available in Project Euclid: 26 October 2015

zbMATH: 1334.57033
MathSciNet: MR3417184
Digital Object Identifier: 10.1215/00127094-3167744

Subjects:
Primary: 57M05
Secondary: 20H10

Rights: Copyright © 2015 Duke University Press

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Vol.164 • No. 14 • 1 November 2015
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