The Moduli of Flat U(p,1) Structures on Riemann Surfaces

Details The Moduli of Flat U(p,1) Structures on Riemann Surfaces The Moduli of Flat U(p,1) Structures on Riemann Surfaces

1999-10-06

arxiv.org/abs/math/9910037v2

Mathematics

Algebraic Geometry

12 pages. The revised version corrects a technical mistake in the previous version in section 4.1

Scientific paper

For a compact Riemann surface $X$ of genus $g > 1$, $\Hom(\pi_1(X), U(p,1))/U(p,1)$ is the moduli space of flat $\U(p,1)$-connections on $X$. There is an integer invariant, $\tau$, the Toledo invariant associated with each element in $\Hom(\pi_1(X), U(p,1))/U(p,1)$. If $q = 1$, then $-2(g-1) \le \tau \le 2(g-1)$. This paper shows that $\Hom(\pi_1(X), U(p,1))/U(p,1)$ has one connected component corresponding to each $\tau \in 2Z$ with $-2(g-1) \le \tau \le 2(g-1)$. Therefore the total number of connected components is $2(g-1) + 1$.

Affiliated with

Also associated with

No associations

Rating

The Moduli of Flat U(p,1) Structures on Riemann Surfaces 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 of Flat U(p,1) Structures on Riemann Surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Moduli of Flat U(p,1) Structures on Riemann Surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-661803