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Immersing Essential Surfaces in Odd Dimensional Closed Hyperbolic Manifolds

Citation

Fu, Lei (2017) Immersing Essential Surfaces in Odd Dimensional Closed Hyperbolic Manifolds. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9XK8CKN. http://resolver.caltech.edu/CaltechThesis:06062017-094601489

Abstract

The surface subgroup theorem, proved by Kahn and Markovic, states that the fundamental group of every closed hyperbolic 3-manifold contains a closed hyperbolic surface subgroup. The criterion of incompressibility, a criterion to ensure that an immersing surface to be essential, has played an important role in their proof.

In this thesis, we generalize the criterion of incompressibility from dimension three to all higher dimensions. Then we use the mixing property of the geodesic flow to construct a closed immersed surface which satisfies the assumption of our criterion when the hyperbolic manifold is in an odd dimension. Together, we prove the surface subgroup theorem in all odd dimensions.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:surface subgroup, incompressible surface, hyperbolic manifold, exponential mixing, ergodic theory, Haken manifold
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Markovic, Vladimir
Thesis Committee:
  • Markovic, Vladimir (chair)
  • Marcolli, Matilde
  • Ni, Yi
  • Zhang, Tengren
Defense Date:7 October 2016
Record Number:CaltechThesis:06062017-094601489
Persistent URL:http://resolver.caltech.edu/CaltechThesis:06062017-094601489
DOI:10.7907/Z9XK8CKN
ORCID:
AuthorORCID
Fu, Lei0000-0003-0076-138X
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10298
Collection:CaltechTHESIS
Deposited By: Lei Fu
Deposited On:07 Jun 2017 00:09
Last Modified:15 Jun 2017 16:59

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