Mathematics

MATHEMATICS COLLOQUIUM Thursday 13 November 2008, 2pm 67-141 Peter Tingley, The University of Melbourne A minus sign that used to annoy me but now I know why it is there Abstract There are (at least) two well known constructions of link invariants. One uses Skein theory: you resolve each crossing of the link as a linear combination of things that don't cross, until you eventually get a linear combination of links with no crossings, which you turn into a polynomial. The other uses quantum groups: you construct a functor from a topological category to some category of representations, in such a way that (oriented framed) links get sent to endomorphisms of the trivial representation, which are just rational functions. Certain instances of these two constructions give rise to essentially the same invariants, but when one carefully matches them there is a minus sign that seems out of place. We will discuss exactly how the constructions match up, and where the minus sign comes from. This talk is largely expository, but we will mention some recent work with Noah Snyder in which we explain other related annoyances in knot theory. All welcome. http://www.maths.uq.edu.au/cdmc/Seminars.html