Type of Culminating Activity
Master of Science in Mathematics
Jens Harlander, Ph.D.
The genus of a graph is the minimal genus of a surface into which the graph can be embedded. Four regular graphs play an important role in low dimensional topology since they arise from curves and virtual knot diagrams. Curves and virtual knots can be encoded combinatorially by certain signed words, called Gauss codes and Gauss paragraphs. The purpose of this thesis is to investigate the genus problem for these combinatorial objects: Given a Gauss word or Gauss paragraph, what is the genus of the curve or virtual knot it represents?
Ross, Bailey Ann, "Combinatorics and Topology of Curves and Knots" (2010). Boise State University Theses and Dissertations. Paper 89.