The complex-symplectic geometry of SL(2,C)-characters over surfaces
| dc.creator | Goldman, William M. | |
| dc.date | 2003-04-21 | |
| dc.date | 2003-10-03 | |
| dc.date.accessioned | 2026-07-07T08:10:19Z | |
| dc.date.available | 2026-07-07T08:10:19Z | |
| dc.description | The SL(2)-character variety X of a closed surface M enjoys a natural complex-symplectic structure invariant under the mapping class group G of M. Using the ergodicity of G on the SU(2)-character variety, we deduce that every G-invariant meromorphic function on X is constant. The trace functions of closed curves on M determine regular functions which generate complex Hamiltonian flows. For simple closed curves, these complex Hamiltonian flows arise from holomorphic flows on the representation variety generalizing the Fenchel-Nielsen twist flows on Teichmueller space and the complex quakebend flows on quasi-Fuchsian space. Closed curves in the complex trajectories of these flows lift to paths in the deformation space of complex-projective structures between different projective structures with the same holonomy (grafting). A pants decomposition determines a holomorphic completely integrable system on X. This integrable system is related to the complex Fenchel-Nielsen coordinates on quasi-Fuchsian space developed by Tan and Kourouniotis, and relate to recent formulas of Platis and Series on complex-length functions and complex twist flows. | |
| dc.identifier | https://arxiv.org/abs/math/0304307 | |
| dc.identifier | http://arxiv.org/abs/math/0304307 | |
| dc.identifier | Algebraic groups and arithmetic, 375--407, Tata Inst. Fund. Res., Mumbai, 2004. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131790 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53D30, 57M50, 58D27 | |
| dc.title | The complex-symplectic geometry of SL(2,C)-characters over surfaces | |
| dc.type | text |