Braid equivalences and the $L$--moves

zbMATH Open1256.57003arXiv1103.4397MaRDI QIDQ2884340

S. Lambropoulou

Publication date: 25 May 2012

Abstract: In this survey paper we present the $L$--moves between braids and how they can adapt and serve for establishing and proving braid equivalence theorems for various diagrammatic settings, such as for classical knots, for knots in knot complements, in c.c.o. 3--manifolds and in handlebodies, as well as for virtual knots, for flat virtuals, for welded knots and for singular knots. The $L$--moves are local and they provide a uniform ground for formulating and proving braid equivalence theorems for any diagrammatic setting where the notion of braid and diagrammatic isotopy is defined, the statements being first geometric and then algebraic.

Full work available at URL: https://arxiv.org/abs/1103.4397

zbMATH Keywords

stabilizationbraidingconjugationMarkov theoremsingular braidsvirtual braids\(L\)-moveslinks in 3-manifoldsmixed braidsmixed linkscommutingwelded braidsbraid equivalencelinks in handlebodieslinks in knot complementstwisted band movetwisted loop conjugation

Mathematics Subject Classification ID

Braid groups; Artin groups (20F36) Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes (57-02)

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