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Diameter bounds on the complex of minimal genus Seifert surfaces for hyperbolic knots

Citation

Pelayo, Roberto Carlos (2007) Diameter bounds on the complex of minimal genus Seifert surfaces for hyperbolic knots. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-06042007-015951

Abstract

Given a link L in the 3-sphere, one can build simplicial complexes MS(L) and IS(L), called the Kakimizu complexes. These complexes have isotopy classes of minimal genus and incompressible Seifert surfaces for L as their vertex sets and have simplicial structures defined via a disjointness property. The Kakimizu complexes enjoy many topological properties and are conjectured to be contractible. Following the work of Gabai on sutured manifolds and Murasugi sums, MS(L) and IS(L) have been classified for various classes of links. This thesis focuses on hyperbolic knots; using minimal surface representatives and Kakimizu's formulation of the path-metric on MS(K), we are able to bound the diameter of this complex in terms of only the genus of the knot. The techniques of this paper are also generalized to one-cusped manifolds with a preferred relative homology class.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:3-manifolds; hyperbolic geometry; minimal surfaces; Seifert surfaces; simplicial complex
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Calegari, Danny C.
Thesis Committee:
  • Calegari, Danny C. (chair)
  • Ramakrishnan, Dinakar
  • Aschbacher, Michael
  • Dunfield, Nathan M.
Defense Date:2 April 2007
Author Email:roberto (AT) caltech.edu
Record Number:CaltechETD:etd-06042007-015951
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-06042007-015951
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2446
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:04 Jun 2007
Last Modified:26 Dec 2012 02:51

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