An SL(2,C) Algebro-Geometric Invariant of Knots
Geometric Topology
2011-12-20 v1
Abstract
In this paper, we define a new algebro-geometric invariant of 3-manifolds resulting from the Dehn surgery along a hyperbolic knot complement in S^3. We establish a Casson type invariant for these 3-manifolds. In the last section, we explicitly calculate the character variety of the figure-eight knot and discuss some applications, as well as the computation of our new invariants for some 3-manifolds resulting from the Dehn surgery along the figure-eight knot.
Keywords
Cite
@article{arxiv.math/0610752,
title = {An SL(2,C) Algebro-Geometric Invariant of Knots},
author = {Weiping Li and Qingxue Wang},
journal= {arXiv preprint arXiv:math/0610752},
year = {2011}
}
Comments
17 pages, revised version of sections 4 and 5 of math.GT/0604057,some computations of the invariant are added