Seminar series
Date
Mon, 29 Apr 2019
15:45
15:45
Location
L6
Speaker
Jacob Rasmussen
Organisation
Cambridge
X.S. Lin defined an invariant of knots in S^3 by counting represenations
of the knot group into SU(2) with fixed meridinal holonomy. Lin's
invariant was subsequently shown to coincide with the Levine-Tristam
signature. I'll define an analogous total Lin invariant which counts
repesentations into both SU(2) and SL_2(R). Unlike the SU(2) version, this
invariant does not (as far as I know) coincide with other known
invariants. I'll describe some applications to left-orderability of Dehn
fillings and branched covers, as well as a curious connection with the
Alexander polynomial. This is joint work with Nathan Dunfield.