English

The volume and Chern-Simons invariant of a representation

Geometric Topology 2019-12-19 v2

Abstract

We give an efficient simplicial formula for the volume and Chern-Simons invariant of a boundary-parabolic PSL(2,C)-representation of a tame 3-manifold. If the representation is the geometric representation of a hyperbolic 3-manifold, our formula computes the volume and Chern-Simons invariant directly from an ideal triangulation with no use of additional combinatorial topology. In particular, the Chern-Simons invariant is computed just as easily as the volume.

Keywords

Cite

@article{arxiv.0710.2049,
  title  = {The volume and Chern-Simons invariant of a representation},
  author = {Christian K. Zickert},
  journal= {arXiv preprint arXiv:0710.2049},
  year   = {2019}
}

Comments

32 pages, 10 figures

R2 v1 2026-06-21T09:29:52.075Z