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- Title
Knot Theory in Handlebodies.
- Authors
Häring-Oldenburg, Reinhard; Lambropoulou, Sofia
- Abstract
We consider oriented knots and links in a handlebody of genus g through appropriate braid representatives in S³, which are elements of the braid groups B[sub 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 Lmoves. The second one uses the Markov moves and conjugation in the groups B[sub g,n.] We show that not all conjugations correspond to istotipies.
- Subjects
KNOT theory; HANDLEBODIES
- Publication
Journal of Knot Theory & Its Ramifications, 2002, Vol 11, Issue 6, p921
- ISSN
0218-2165
- Publication type
Article