A Hyperelliptic View on Teichmuller Space. I

Details A Hyperelliptic View on Teichmuller Space. I A Hyperelliptic View on Teichmuller Space. I

2007-09-11

arxiv.org/abs/0709.1711v2

Mathematics

Geometric Topology

25 pages, 44 figures, exposition slightly improved

Scientific paper

We explicitly describe the Teichmuller space TH_n of hyperelliptic surfaces in terms of natural and effective coordinates as the space of certain (2n-6)-tuples of distinct points on the ideal boundary of the Poincare disc. We essentially use the concept of a simple earthquake which is a particular case of a Fenchel-Nielsen twist deformation. Such earthquakes generate a group that acts transitively on TH_n. This fact can be interpreted as a continuous analog of the well-known Dehn theorem saying that the mapping class group is generated by Dehn twists. We find a simple and effective criterion that verifies if a given representation of the surface group \pi_1\Sigma in the group of isometries of the hyperbolic plane is faithful and discrete. The article also contains simple and elementary proofs of several known results, for instance, of W. M. Goldman's theorem [Gol1] characterizing the faithful discrete representations as having maximal Toledo invariant (which is essentially the area of the representation in the two-dimensional case).

Affiliated with

Also associated with

No associations

Rating

A Hyperelliptic View on Teichmuller Space. I 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 A Hyperelliptic View on Teichmuller Space. I, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Hyperelliptic View on Teichmuller Space. I will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-21499