The Moduli of Flat U(p,1) Structures on Riemann Surfaces
| dc.creator | Xia, Eugene Z. | |
| dc.date | 1999-10-06 | |
| dc.date | 1999-12-21 | |
| dc.date.accessioned | 2026-07-07T05:31:05Z | |
| dc.date.available | 2026-07-07T05:31:05Z | |
| dc.description | For a compact Riemann surface $X$ of genus $g > 1$, $\Hom(π_1(X), U(p,1))/U(p,1)$ is the moduli space of flat $\U(p,1)$-connections on $X$. There is an integer invariant, $τ$, the Toledo invariant associated with each element in $\Hom(π_1(X), U(p,1))/U(p,1)$. If $q = 1$, then $-2(g-1) \le τ\le 2(g-1)$. This paper shows that $\Hom(π_1(X), U(p,1))/U(p,1)$ has one connected component corresponding to each $τ\in 2Z$ with $-2(g-1) \le τ\le 2(g-1)$. Therefore the total number of connected components is $2(g-1) + 1$. | |
| dc.description | 12 pages. The revised version corrects a technical mistake in the previous version in section 4.1 | |
| dc.identifier | https://arxiv.org/abs/math/9910037 | |
| dc.identifier | http://arxiv.org/abs/math/9910037 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79214 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14D20;14H60 | |
| dc.title | The Moduli of Flat U(p,1) Structures on Riemann Surfaces | |
| dc.type | text |