Date of Final Oral Examination (Defense)


Type of Culminating Activity


Degree Title

Master of Science in Mathematics



Major Advisor

Jens Harlander, Ph.D.

Second Advisor

Andrés Caicedo

Third Advisor

Uwe Kaiser


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.