Pants Decompositions of Surfaces
| dc.creator | Hatcher, Allen | |
| dc.date | 1999-06-12 | |
| dc.date.accessioned | 2026-07-07T05:29:29Z | |
| dc.date.available | 2026-07-07T05:29:29Z | |
| dc.description | We consider collections of disjoint simple closed curves in a compact orientable surface which decompose the surface into pairs of pants. The isotopy classes of such curve systems form the vertices of a 2-complex, whose edges correspond to certain simple moves in which only one curve changes, and whose 2-cells correspond to certain elementary cycles of simple moves. The main theorem is that this 2-complex is simply-connected. Thus any two pants decompositions of a surface are joinable by a sequence of simple moves, and any two such sequences of simple move are related by the elementary relations. The proof is similar to the proof, in a 1980 paper with W. Thurston, of an analogous result for curve systems with connected genus zero complement. [The present paper is essentially an excerpt from a joint paper with P. Lochak and L. Schneps which is to appear in Crelle's Journal.] | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/9906084 | |
| dc.identifier | http://arxiv.org/abs/math/9906084 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78654 | |
| dc.subject | Geometric Topology | |
| dc.title | Pants Decompositions of Surfaces | |
| dc.type | text |