KNOT THEORY IN HANDLEBODIES-Reference-Cited by-同舟云学术

KNOT THEORY IN HANDLEBODIES

Published:2002-09 Issue:06 Volume:11 Page:921-943
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

HÄRING-OLDENBURG REINHARD¹,LAMBROPOULOU SOFIA²

Affiliation:

1. Mathematisches Institut, Göttingen Universität, Bunsenstrasse 3-5, D-37073 Göttingen, Germany

2. Department of Mathematics, National Technical University of Athens, Zografou Campus, GR-15780 Athens, Greece

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 Bg,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 Bg,n. We show that not all conjugations correspond to isotopies.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216502002050

Reference15 articles.

1. An invariant of dichromatic links

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