The Lickorish-Wallace Theorem
OPEN ACCESS
Loading...
Author / Producer
Date
2024-06
Publication Type
Bachelor Thesis
ETH Bibliography
yes
Citations
Altmetric
OPEN ACCESS
Data
Rights / License
Abstract
In this bachelor’s thesis, we prove a theorem discovered independently by W. B. R. Lickorish [Lic62] and by Andrew H. Wallace [Wal62] in 1962. It states, that any closed, connected, and orientable 3-manifold can be obtained by Dehn-surgery on a link in S^3. We will formalize the proof given by Lickorish. It relies heavily on the Lickorish twist-theorem, stating that the mapping class group of a genus-g surface is generated by Dehn-twists about simple closed curves.
In the first part of this thesis, we will give a brief introduction to differential topology. The goal of the second part will be to introduce mapping class groups of surfaces and prove the Lickorish twist-theorem. The third and final parts objective will be to prove the fundamental theorem of Lickorish and Wallace mentioned above.
Permanent link
Publication status
published
External links
Editor
Contributors
Examiner : Lewark, Lukas
Book title
Journal / series
Volume
Pages / Article No.
Publisher
ETH Zurich
Event
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Mapping class group; Dehn twist; Heegaard splitting; Surgery on links; Isotopy
Organisational unit
01404 - BSc Mathematik / BSc Mathematics