(1,1)-knots via the mapping class group of the twice punctured torus
| dc.creator | Cattabriga, Alessia | |
| dc.creator | Mulazzani, Michele | |
| dc.date | 2002-05-13 | |
| dc.date | 2004-04-06 | |
| dc.date.accessioned | 2026-07-07T04:48:28Z | |
| dc.date.available | 2026-07-07T04:48:28Z | |
| dc.description | We develop an algebraic representation for (1,1)-knots using the mapping class group of the twice punctured torus MCG(T,2). We prove that every (1,1)-knot in a lens space L(p,q) can be represented by the composition of an element of a certain rank two free subgroup of MCG(T,2) with a standard element only depending on the ambient space. As a notable examples, we obtain a representation of this type for all torus knots and for all two-bridge knots. Moreover, we give explicit cyclic presentations for the fundamental groups of the cyclic branched coverings of torus knots of type (k,ck+2). | |
| dc.description | 18 pages, 10 figures. New version with minor changes. Accepted for publication in Advances in Geometry | |
| dc.identifier | https://arxiv.org/abs/math/0205138 | |
| dc.identifier | http://arxiv.org/abs/math/0205138 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64058 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M05; 20F38 | |
| dc.title | (1,1)-knots via the mapping class group of the twice punctured torus | |
| dc.type | text |