Closed surfaces in knot complements and 3-manifolds

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2024

Author dc:creator

• Basilio, Brannon

Contributors dc:contributor

• Dunfield, Nathan
• Hirani, Anil
• Rasmussen, Jake
• Rasmussen, Sarah

• Essential Surfaces
• Knot Complements
• 3-manifolds

Statement dc:rights

• Copyright 2024 Brannon Basilio

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/124319

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F124319