Publication Date
5-2012
Type of Culminating Activity
Thesis
Degree Title
Master of Science in Mathematics
Department
Mathematics
Major Advisor
Jens Harlander, Ph.D.
Advisor
Andrés Caicedo
Advisor
Uwe Kaiser
Abstract
The Dehn complex of prime, alternating virtual links has been shown to be non-positively curved in the paper "Generalized knot complements and some aspherical ribbon disc complements" by J. Harlander and S. Rosebrock (2003) [7]. This thesis investigates the geometry of an arbitrary alternating virtual link. A method is constructed for which the Dehn complex of any alternating virtual link may be decomposed into Dehn complexes with non-positive curvature. We further study the relationship between the Dehn space and Wirtinger space, and we relate their fundamental groups using generating curves on surfaces. We conclude with interesting examples of Dehn complexes of virtual link diagrams, which illustrate our findings.
Recommended Citation
Byrd, Rachel Elizabeth, "On the Geometry of Virtual Knots" (2012). Boise State University Theses and Dissertations. 263.
https://scholarworks.boisestate.edu/td/263