| | |
| | |
Stat |
Members: 3645 Articles: 2'501'711 Articles rated: 2609
19 April 2024 |
|
| | | |
|
Article overview
| |
|
Representations of the fundamental group of a surface in PU(p,q) and holomorphic triples | Steven B. Bradlow
; Oscar Garcia-Prada
; Peter B. Gothen
; | Date: |
13 Jul 2001 | Journal: | C. R. Acad. Sci. Paris Sér. I Math. 333 (2001), 347-352 | Subject: | Algebraic Geometry; Representation Theory MSC-class: 14D20 (Primary) 14F45, 14H60, 32G13 (Secondary) | math.AG math.RT | Affiliation: | University of Illinois, Universidad Autonoma de Madrid, Universidade do Porto | Abstract: | We count the connected components in the moduli space of PU(p,q)-representations of the fundamental group for a closed oriented surface. The components are labelled by pairs of integers which arise as topological invariants of the flat bundles associated to the representations. Our results show that for each allowed value of these invariants, which are bounded by a Milnor-Wood type inequality, there is a unique non-empty connected component. Interpreting the moduli space of representations as a moduli space of Higgs bundles, we take a Morse theoretic approach using a certain smooth proper function on the Higgs moduli space. 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 non-empty and irreducible. | Source: | arXiv, math.AG/0107103 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |