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AN SL₂(ℂ) ALGEBRO-GEOMETRIC INVARIANT OF KNOTS

WEIPING LI

Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, USA

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and

QINGXUE WANG

School of Mathematical Sciences, Fudan University, Shanghai 200433, P. R. China

Corresponding author.

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https://doi.org/10.1142/S0129167X11007240Cited by:2 (Source: Crossref)

Abstract

In this paper, we define a new algebro-geometric invariant of three-manifolds resulting from Dehn surgery along a hyperbolic knot complement in S³. 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.

Keywords:

AMSC: 57M25, 57M27, 14H50

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