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Homology of curves and surfaces in closed hyperbolic 3-manifolds

Liu, Yi and Markovic, Vladimir (2015) Homology of curves and surfaces in closed hyperbolic 3-manifolds. Duke Mathematical Journal, 164 (14). pp. 2723-2808. ISSN 0012-7094. doi:10.1215/00127094-3167744.

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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 π_1-injectively immersed quasi-Fuchsian subsurface. Second, every rationally null-homologous, π_1-injectively immersed oriented closed 1-submanifold in a closed hyperbolic 3-manifold has an equidegree finite cover which bounds an oriented connected compact π_1-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.

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Additional Information:© 2015 Duke University Press. Received 12 November 2013. Revision received 7 December 2014. The authors thank Hongbin Sun for pointing out errors in a previous draft of this article and Danny Calegari for valuable comments. The authors also thank the anonymous referees for suggestions and corrections. The authors’ work was supported by National Science Foundation grant DMS 1308836.
Funding AgencyGrant Number
NSFDMS 1308836
Issue or Number:14
Classification Code:2010 Mathematics Subject Classification. Primary 57M05; Secondary 20H10
Record Number:CaltechAUTHORS:20151201-095003953
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:62492
Deposited By: Tony Diaz
Deposited On:03 Dec 2015 03:22
Last Modified:10 Nov 2021 23:03

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