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Immersed Surfaces, Dehn Surgery and Essential Laminations

Citation

Li, Tao (2000) Immersed Surfaces, Dehn Surgery and Essential Laminations. Dissertation (Ph.D.), California Institute of Technology. https://resolver.caltech.edu/CaltechTHESIS:11212019-175145827

Abstract

Let M be an orientable and irreducible 3-manifold whose boundary is an incompressible torus. We are interested in immersed essential surfaces in closed 3-manifolds obtained from Dehn fillings on M. We show the following two things.

In Chapter 2, we suppose that M does not contain closed non-peripheral incompressible surfaces. We show that the immersed surfaces in M with the 4-plane property can realize only finitely many slopes. Moreover, we show that only finitely many Dehn fillings on M can yield 3-manifolds that admit non-positive cubing. This gives the first examples of hyperbolic 3-manifolds that cannot admit non-positive cubing.

In Chapter 3, we suppose M is hyperbolic. We show that all but finitely many Dehn fillings on M yield 3-manifolds that contain closed essential surfaces. Moreover, we give a bound on the number of exceptional Dehn fillings.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Gabai, David
Thesis Committee:
  • Gabai, David (chair)
  • Bonahon, Francis
  • Candel, Alberto
  • Pandharipande, Rahul
Defense Date:22 May 2000
Record Number:CaltechTHESIS:11212019-175145827
Persistent URL:https://resolver.caltech.edu/CaltechTHESIS:11212019-175145827
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13595
Collection:CaltechTHESIS
Deposited By: Melissa Ray
Deposited On:22 Nov 2019 17:46
Last Modified:02 Dec 2020 02:45

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