Homological action of the modular group on some cubic moduli spaces
| dc.creator | Goldman, William M. | |
| dc.creator | Neumann, Walter D. | |
| dc.date | 2004-02-03 | |
| dc.date.accessioned | 2026-07-07T08:10:19Z | |
| dc.date.available | 2026-07-07T08:10:19Z | |
| dc.description | We describe the action of the automorphism group of the complex cubic x^2+y^2+z^2-xyz-2 on the homology of its fibers. This action includes the action of the mapping class group of a punctured torus on the subvarieties of its SL(2,C) character variety given by fixing the trace of the peripheral element (so-called "relative character varieties"). This mapping class group is isomorphic to PGL(2,Z). We also describe the corresponding mapping class group action for the four-holed sphere and its relative SL(2,C) character varieties, which are fibers of deformations x^2+y^2+z^2-xyz-2-Px-Qy-Rz of the above cubic. The 2-congruence subgroup PGL(2,Z)_(2) still acts on these cubics and is the full automorphism group when P,Q,R are distinct. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0402039 | |
| dc.identifier | http://arxiv.org/abs/math/0402039 | |
| dc.identifier | Math. Res. Lett. 12 (2005), no. 4, 575--591 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131791 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M05, 30F60, 20H10 | |
| dc.title | Homological action of the modular group on some cubic moduli spaces | |
| dc.type | text |