Knot theory in handlebodies
| dc.creator | Haering-Oldenburg, Reinhard | |
| dc.creator | Lambropoulou, Sofia | |
| dc.date | 2004-05-26 | |
| dc.date.accessioned | 2026-07-07T05:08:37Z | |
| dc.date.available | 2026-07-07T05:08:37Z | |
| dc.description | We consider oriented knots and links in a handlebody of genus $g$ through appropriate braid representatives in $S^3$, which are elements of the braid groups $B_{g,n}$. We prove a geometric version of the Markov theorem for braid equivalence in the handlebody, which is based on the $L$-moves. Using this we then prove two algebraic versions of the Markov theorem. The first one uses the $L$-moves. The second one uses the Markov moves and conjugation in the groups $B_{g,n}$. We show that not all conjugations correspond to isotopies. | |
| dc.description | 23 pages, 23 figures, LaTex file | |
| dc.identifier | https://arxiv.org/abs/math/0405502 | |
| dc.identifier | http://arxiv.org/abs/math/0405502 | |
| dc.identifier | J. Knot Theory and Ramifications, Vol. 11, No. 6, pp. 921--943 (2002) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71334 | |
| dc.subject | Geometric Topology | |
| dc.subject | Algebraic Topology | |
| dc.subject | 57M25 | |
| dc.title | Knot theory in handlebodies | |
| dc.type | text |