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L-MOVES AND MARKOV THEOREMS

SOFIA LAMBROPOULOU

Department of Mathematics, National Technical University of Athens, Zografou campus, GR-157 80 Athens, Greece

https://doi.org/10.1142/S0218216507005919Cited by:7 (Source: Crossref)

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:

AMSC: 57M25, 57M27, 57N10

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