Non-triviality of the MM-degree of the AA-polynomial

This note gives a proof that the $A$-polynomial of any nontrivial knot in $S^3$ has nontrivial $M$-degree.Comment: 5 page

Concordance group of virtual knots

We study concordance of virtual knots. Our main result is that a classical knot K is virtually slice if and only if it is classically slice. From this we deduce that the concordance group of classical knots embeds into the concordance group of long virtual knots

A connected sum formula for the SU(3) Casson invariant

We provide a formula for the SU(3) Casson invariant for 3-manifolds given as the connected sum of two integral homology 3-spheres.Comment: 14 page

The SU(3) Casson Invariant for Integral Homology 3-Spheres

We derive a gauge theoretic invariant of integral homology 3-spheres which counts gauge orbits of irreducible, perturbed flat SU(3) connections with sign given by spectral flow. To compensate for the dependence of this sum on perturbations, the invariant includes contributions from the reducible, perturbed flat orbits. Our formula for the correction term generalizes that given by Walker in his extension of Casson's SU(2) invariant to rational homology 3-spheres.Comment: 63 pages, 2 figures, to appear in J. Diff. Geo