Timeline for Representations of surface groups via holomorphic connections
Current License: CC BY-SA 2.5
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 17, 2009 at 10:43 | comment | added | Jack Evans | Hitchin fixes a curve or equivalently representation of $\Gamma$ in $PSL(2,\mathbb{R})$ and uses it to identify the cotangent bundle of the space of $SU(2)$ representations with the space of $SL(2,\mathbb{C})$ representations of $\Gamma$. Joel's construction fixes a local system or equivalently a representation of $Gamma$ in $SU(2)$ and uses it to map the cotangent bundle of the space of $PSL(2,\mathbb{R})$ representations to the space of $SL(2,\mathbb{C}) representations. This is a clearer statement of what I was guessing at yesterday and explains the coincidence of dimensions. | |
| Dec 15, 2009 at 19:33 | comment | added | Dmitri Panov | A holomorphic bundle on a surface that admits a flat connection with a non-trivial monodromy in SU(2) is never holomorphically trivial. Joel's question is not about Kobayashi-Hitchin correspondece, it is "orthogonal" to Hitchin's paper. Notice also that the question is about repesentations in $SL(2,C)$ rather than $SL(2,R)$. | |
| Dec 15, 2009 at 19:21 | history | answered | Jack Evans | CC BY-SA 2.5 |