Circle packings on surfaces with projective structures and uniformization

Details Circle packings on surfaces with projective structures and uniformization Circle packings on surfaces with projective structures and uniformization

2003-08-15

arxiv.org/abs/math/0308147v1

Pacific J. Math. 225 (2006), no. 2, 287--300

Mathematics

Geometric Topology

14 pages, 11 embedded figures

Scientific paper

Let \Sigma_g be a closed orientable surface of genus g \geq 2 and \tau a graph on \Sigma_g with one vertex which lifts to a triangulation of the universal cover. We have shown that the cross ratio parameter space \mathcal{C}_\tau associated with \tau, which can be identified with the set of all pairs of a projective structure and a circle packing on it with nerve isotopic to \tau, is homeomorphic to \mathbb{R}^{6g-6}, and moreover that the forgetting map of \mathcal{C}_\tau to the space of projective structures is injective. In this paper, we show that the composition of the forgetting map with the uniformization from \mathcal{C}_\tau to the Teichm\"uller space \mathcal{T}_g is proper.

Affiliated with

Also associated with

No associations

Rating

Circle packings on surfaces with projective structures and uniformization 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 Circle packings on surfaces with projective structures and uniformization, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Circle packings on surfaces with projective structures and uniformization will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-329381