71 research outputs found
Non-triviality of the -degree of the -polynomial
This note gives a proof that the -polynomial of any nontrivial knot in
has nontrivial -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
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