Universal formulae for SU(n) casson invariants of knots

An SU(n) Casson invariant of a knot is an integer which can be thought of as an algebraic-topological count of the number of characters of SU(n) representations of the knot group which take a longitude into a given conjugacy class. For fibered knots, these invariants can be characterized as Lefschetz numbers which, for generic conjugacy classes, can be computed using a recursive algorithm of Atiyah and Bott, as adapted by Frohman. Using a new …