Complex Volume of Hyperbolic Knots

Associated to a hyperbolic knot, there is a naturally defined hyperbolic volume. The imaginary part of the hyperbolic volume determines the Chern-Simons Invariant.

Walter Neumann provided us with a complete set of data for knots of 12 or fewer crossings, using the program Snap.

References

[1] Robert Meyerhoff: "Geometric invariants of 3-manifolds," Math. Intelligencer 14 (1992), 37-153.

[2] W.D. Neumann, Extended Bloch group and the Cheeger-Chern-Simons class, Geom. Topol. 8 (2004), 413-474.

[3] W.D. Neumann, D. Zagier, Volumes of hyperbolic 3-manifolds, Topology 24 (1985) 307-332.