On Volumes and Chern-Simons Invariants of Geometric 3-Manifolds
Vol. 3 (1996), No. 3, Page 723--744.
Hilden, Hugh M. ; Lozano, MarÃa Teresa ; Montesinos-Amilibia, José MarÃa
On Volumes and Chern-Simons Invariants of Geometric 3-Manifolds
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]
Abstract:
Let $M_n(K)$ be the hyperbolic 3-manifold obtained by $n$-cyclic covering of $S^3$ branched over a hyperbolic knot $K$. A method to compute the volume and the Chern-Simons invariant of $M_n(K)$ is given. The value of the volume of $M_n$ is $n$ times the value of the volume of the corresponding hyperbolic orbifold. This volume can be obtained by appying the Schläffli Formula for the volume to the cone-manifold family, $(K,α )$, with singularity $K$. The same approch is followed for the Chern-Simons invariant, after proving a "Schläffli Formula" for a generalized Chern-Simons function on the family of cone-manifold structures $(K,α )$.
Mathematics Subject Classification (1991): Primary 57M50, 51M10, 51M25
Mathematical Reviews Number: MR1432115
Received: 1996-04-08
