Vol. 249, No. 2, 2011

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SL2()-character variety of a hyperbolic link and regulator

Weiping Li and Qingxue Wang

Vol. 249 (2011), No. 2, 385–404

We analyze a special smooth projective variety Y h arising from some one-dimensional irreducible slices on the SL2()-character variety of a hyperbolic link in S3. We prove that a natural symbol obtained from these one-dimensional slices is a torsion in K2((Y h)). By using the regulator map from K2 to the corresponding Deligne cohomology, we get some variation formulas on some Zariski open subset of Y h. From this we discuss a possible parametrized volume conjecture for both hyperbolic links and knots.

Chern–Simons invariant, character variety, algebraic K-theory, hyperbolic links, volume conjecture, regulator map
Mathematical Subject Classification 2000
Primary: 57M25, 57M27
Secondary: 19F15, 14H50
Received: 9 December 2009
Accepted: 9 September 2010
Published: 1 February 2011
Weiping Li
Department of Mathematics
Oklahoma State University
Stillwater, OK 74078
United States
Qingxue Wang
School of Mathematical Sciences
Fudan University
Shanghai 200433