The moduli space of Riemann surfaces is Kahler hyperbolic

Details The moduli space of Riemann surfaces is Kahler hyperbolic The moduli space of Riemann surfaces is Kahler hyperbolic

2000-10-02

arxiv.org/abs/math/0010022v1

Ann. of Math. (2) 151 (2000), no. 1, 327--357

Mathematics

Complex Variables

31 pages

Scientific paper

Let $\cM_{g,n}$ be the moduli space of Riemann surfaces of genus $g$ with $n$ punctures. From a complex perspective, moduli space is hyperbolic. For example, $\cM_{g,n}$ is abundantly populated by immersed holomorphic disks of constant curvature -1 in the Teichm\"uller (=Kobayashi) metric. When $r=\dim_{\cx} \cM_{g,n}$ is greater than one, however, $\cM_{g,n}$ carries no complete metric of bounded negative curvature. Instead, Dehn twists give chains of subgroups $\zed^r \subset \pi_1(\cM_{g,n})$ reminiscent of flats in symmetric spaces of rank $r>1$. In this paper we introduce a new K\"ahler metric on moduli space that exhibits its hyperbolic tendencies in a form compatible with higher rank.

Affiliated with

Also associated with

No associations

Rating

The moduli space of Riemann surfaces is Kahler hyperbolic 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 moduli space of Riemann surfaces is Kahler hyperbolic, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The moduli space of Riemann surfaces is Kahler hyperbolic will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-531177