The complex volume of SL(n,C)-representations of 3-manifolds

Details The complex volume of SL(n,C)-representations of 3-manifolds The complex volume of SL(n,C)-representations of 3-manifolds

2011-11-11

arxiv.org/abs/1111.2828v1

Mathematics

Geometric Topology

43 pages, 11 figures

Scientific paper

For a compact 3-manifold M with arbitrary (possibly empty) boundary, we give a parametrization of the set of conjugacy classes of boundary-unipotent representations of the fundamental group of M into SL(n,C). Our parametrization uses Ptolemy coordinates, which are inspired by coordinates on higher Teichmueller spaces due to Fock and Goncharov. We show that a boundary-unipotent representation determines an element in Neumann's extended Bloch group, and use this to obtain an efficient formula for the Cheeger-Chern-Simons invariant, and in particular for the volume. Computations for the census manifolds show that boundary-unipotent representations are abundant, and numerical comparisons with census volumes, suggest that the volume of a representation is an integral linear combination of volumes of hyperbolic 3-manifolds. This is in agreement with a conjecture of Walter Neumann, stating that the Bloch group is generated by hyperbolic manifolds.

Affiliated with

Also associated with

No associations

Rating

The complex volume of SL(n,C)-representations of 3-manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The complex volume of SL(n,C)-representations of 3-manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The complex volume of SL(n,C)-representations of 3-manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-140234