Topics in knot theory : on generalized crossing changes and the additivity of the Turaev genus
We first study cosmetic crossing changes and cosmetic generalized crossing changes in knots of genus one, satellite knots, and knots obtained via twisting operations on standardly embedded tori in the knot complement. As a result, we find obstructions to the existence of cosmetic generalized crossing changes in several large families of knots. We then study Turaev surfaces and use decomposing spheres to analyze the additivity of the Turaev genus for the summands of composite knots with Turaev genus one.
Read
- In Collections
-
Electronic Theses & Dissertations
- Copyright Status
- In Copyright
- Material Type
-
Theses
- Authors
-
Balm, Cheryl Lyn Jaeger
- Thesis Advisors
-
Kalfagianni, Efstratia
- Committee Members
-
Hedden, Matthew
Bell, Robert
Schmidt, Ben
Fintushel, Ron
- Date
- 2013
- Program of Study
-
Mathematics - Doctor of Philosophy
- Degree Level
-
Doctoral
- Language
-
English
- Pages
- xiii, 97 pages
- ISBN
-
9781303062667
1303062666
- Permalink
- https://doi.org/doi:10.25335/M5448Q