An SL(2,C) Algebro-Geometric Invariant of Knots

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.

arXiv comment17 pages, revised version of sections 4 and 5 of math.GT/0604057,some computations of the invariant are added