L-MOVES AND MARKOV THEOREMS
- 1 December 2007
- journal article
- Published by World Scientific Pub Co Pte Ltd in Journal of Knot Theory and Its Ramifications
- Vol. 16 (10), 1459-1468
- https://doi.org/10.1142/s0218216507005919
Abstract
Given a knot theory (virtual, singular, knots in a 3-manifold etc.), there are deep relations between the diagrammatic knot equivalence in this theory, the braid structures and a corresponding braid equivalence. The L-moves between braids, due to their fundamental nature, may be adapted to any diagrammatic situation in order to formulate a corresponding braid equivalence. In this short paper, we discuss and compare various diagrammatic set-ups and results therein, in order to draw the underlying logic relating diagrammatic isotopy, braid structures, Markov theorems and L-move analogues. Finally, we apply our conclusions to singular braids.Keywords
This publication has 15 references indexed in Scilit:
- Virtual braidsFundamenta Mathematicae, 2004
- KNOT THEORY IN HANDLEBODIESJournal of Knot Theory and Its Ramifications, 2002
- Virtual Knot TheoryEuropean Journal of Combinatorics, 1999
- Singular Braids and Markov's TheoremJournal of Knot Theory and Its Ramifications, 1997
- The braid-permutation groupTopology, 1997
- New points of view in knot theoryBulletin of the American Mathematical Society, 1993
- Invariants of graphs in three-spaceTransactions of the American Mathematical Society, 1989
- Hecke Algebra Representations of Braid Groups and Link PolynomialsAnnals of Mathematics, 1987
- Theorie der ZöpfeAbhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, 1925
- A Lemma on Systems of Knotted CurvesProceedings of the National Academy of Sciences of the United States of America, 1923