The Dimension of the Torelli group
| dc.creator | Bestvina, Mladen | |
| dc.creator | Bux, Kai-Uwe | |
| dc.creator | Margalit, Dan | |
| dc.date | 2007-09-03 | |
| dc.date.accessioned | 2026-07-07T08:27:18Z | |
| dc.date.available | 2026-07-07T08:27:18Z | |
| dc.description | We prove that the cohomological dimension of the Torelli group for a closed connected orientable surface of genus g at least 2 is equal to 3g-5. This answers a question of Mess, who proved the lower bound and settled the case of g=2. We also find the cohomological dimension of the Johnson kernel (the subgroup of the Torelli group generated by Dehn twists about separating curves) to be 2g-3. For g at least 2, we prove that the top dimensional homology of the Torelli group is infinitely generated. Finally, we give a new proof of the theorem of Mess that gives a precise description of the Torelli group in genus 2. The main tool is a new contractible complex, called the "complex of cycles", on which the Torelli group acts. | |
| dc.description | 39 pages, 9 figures | |
| dc.identifier | https://arxiv.org/abs/0709.0287 | |
| dc.identifier | http://arxiv.org/abs/0709.0287 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137227 | |
| dc.subject | Geometric Topology | |
| dc.subject | Group Theory | |
| dc.subject | 20F34; 57M07 | |
| dc.title | The Dimension of the Torelli group | |
| dc.type | text |