Mathematics – Geometric Topology
Scientific paper
2003-04-02
Mathematics
Geometric Topology
24 pages, submitted
Scientific paper
We classify the connected components of the space of representations of the fundamental group of a closed oriented surface of genus $\geq 2$ in $Sp(4,{\mathbf R})$. We prove that this is equivalent to classifying the connected components of the moduli space of representations (which consists of conjugacy classes of reductive representations). We then continue the analysis initiated by Gothen in math/9904114, relying on: (1) the relation between our moduli space of representations and the moduli space of certain (polystable) analogues of Higgs bundles (which follows essentially from work of Hitchin, Simpson and Corlette) and (2) the existence of a proper function on the moduli space whose set of local minima can be identified with the moduli space $N$ of (polystable) quadratic bundles of rank 2; we finally deduce our result from the classification of the connected components of $N$.
Garcia-Prada Oscar
Riera Ignasi Mundet i.
No associations
LandOfFree
Representations of the fundamental group of a closed oriented surface in Sp(4,R) 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 Representations of the fundamental group of a closed oriented surface in Sp(4,R), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Representations of the fundamental group of a closed oriented surface in Sp(4,R) will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-125434