AN SL2(C) ALGEBRO-GEOMETRIC INVARIANT OF KNOTS

作者:Li Weiping*; Wang Qingxue
来源:International Journal of Mathematics, 2011, 22(9): 1209-1230.
DOI:10.1142/S0129167X11007240

摘要

In this paper, we define a new algebro-geometric invariant of three-manifolds resulting from Dehn surgery along a hyperbolic knot complement in S-3. We establish a Casson-type invariant for these three-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 three-manifolds resulting from Dehn surgery along the figure-eight knot.

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