Mathematics – Algebraic Geometry
Scientific paper
2002-06-03
Mathematics
Algebraic Geometry
106 pages
Scientific paper
Using the $L^2$ norm of the Higgs field as a Morse function, we study the moduli spaces of $U(p,q)$-Higgs bundles over a Riemann surface. We require that the genus of the surface be at least two, but place no constraints on $(p,q)$. A key step is the identification of the function's local minima as moduli spaces of holomorphic triples. We prove that these moduli spaces of triples are irreducible and non-empty. Because of the relation between flat bundles and fundamental group representations, we can interpret our conclusions as results about the number of connected components in the moduli space of semisimple $PU(p,q)$-representations. The topological invariants of the flat bundles bundle are used to label components. These invariants are bounded by a Milnor-Wood type inequality. For each allowed value of the invariants satisfying a certain coprimality condition, we prove that the corresponding component is non-empty and connected. If the coprimality condition does not hold, our results apply to the irreducible representations.
Bradlow Steven B.
Garcia-Prada Oscar
Gothen Peter B.
No associations
LandOfFree
Surface group representations, Higgs bundles, and holomorphic triples 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 Surface group representations, Higgs bundles, and holomorphic triples, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Surface group representations, Higgs bundles, and holomorphic triples will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-693457