SU(2) representations of knot groups

ABSTRACT Ph.D. Thesis SU(2) REPRESENTATIONS OF KNOT GROUPS TANGÜL UYGUR Anadolu University Graduate School of Natural and Applied Sciences, Mathematics Program Supervisor: Assoc. Prof. Hüseyin AZCAN 2002,73 Pages In this study, the characterization of the topological type of the irreducible SU(2) representations of a particular class of knot groups was undertaken. To the best of our knowledge, there is no study so far towards the structure of SU(2) representation space of the knot groups in general, the two bridge knots in particular. Here, in this thesis, it was shown that the representation space of an n tangle where n is an odd integer is disjoint union of - - - - - arcs where A(-l) is the Alexander polynomial of the knot evaluated at -1. Later, a characterization of the topology of the space of representation of a 2-bridge knot of type (2,n) was given. It was also shown that this space is the disjoint n-\ union of an open arc and circles when n is an odd integer whereas it is the disjoint n union of - circles when n is an even integer. While constructing the elements of the representation space, a detailed exposition of the method was also given. Keywords: The knot group, SU(2) representation of the knot group, spherical geometry. u