Advisor(s) - Committee Chair
Dr. Claus Ernst (Director), Dr. Uta Ziegler, and Dr. Lan Nguyen
Department of Mathematics
Master of Science
This thesis introduces a new quantity called loop number, and shows the conditions in which loop numbers become knot invariants. For a given knot diagram D, one can traverse the knot diagram and count the number of loops created by the traversal. The number of loops recorded depends on the starting point in the diagram D and on the traversal direction. Looking at the minimum or maximum number of loops over all starting points and directions, one can define two positive integers as loop numbers of the diagram D. In this thesis, the conditions under which these loop numbers become knot invariants are identified. In particular, the thesis answers the question when these numbers are invariant under flypes in the diagram D.
Geometry and Topology
Pham, Van Anh, "Loop Numbers of Knots and Links" (2017). Masters Theses & Specialist Projects. Paper 1952.