Closed surfaces in knot complements and 3-manifolds
Basilio, Brannon
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https://hdl.handle.net/2142/124319
Description
Title
Closed surfaces in knot complements and 3-manifolds
Author(s)
Basilio, Brannon
Issue Date
2024-04-20
Director of Research (if dissertation) or Advisor (if thesis)
Dunfield, Nathan
Doctoral Committee Chair(s)
Hirani, Anil
Committee Member(s)
Rasmussen, Jake
Rasmussen, Sarah
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
essential surfaces
knot complements
3-manifolds
Abstract
Closed essential surfaces play a key role in the study of the geometry and topology of knots and, more generally, 3-manifolds. This thesis gives several results concerning such objects including a closed form for the number of closed essential surfaces in certain Montesinos knot complements and an algorithm of finding closed totally geodesic surfaces in knot complements and 3-manifolds.
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