Garside theory and subsurfaces: some examples in braid groups
| Autor: | Bert Wiest, Saul Schleimer |
|---|---|
| Přispěvatelé: | Warwick Mathematics Institute (WMI), University of Warwick [Coventry], Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Polynomial
Pure mathematics Computer Networks and Communications Conjugacy problem Braid group Group Theory (math.GR) 01 natural sciences [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR] 20F65 20F36 20F10 Mathematics::Group Theory Mathematics - Geometric Topology Conjugacy class Projection (mathematics) [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] Mathematics::Category Theory Mathematics::Quantum Algebra 0103 physical sciences Braid FOS: Mathematics 0101 mathematics QA Mathematics Applied Mathematics 010102 general mathematics Geometric Topology (math.GT) Mathematics::Geometric Topology Computational Mathematics Computational Theory and Mathematics Bounded function 010307 mathematical physics Constant (mathematics) Mathematics - Group Theory |
| Zdroj: | Groups-Complexity-Cryptology Groups-Complexity-Cryptology, De Gruyter, 2019, 11 (2), pp.61-75. ⟨10.1515/gcc-2019-2007⟩ journal of Groups, Complexity, Cryptology journal of Groups, Complexity, Cryptology, 2019, 11 (2), pp.61-75. ⟨10.1515/gcc-2019-2007⟩ |
| ISSN: | 1867-1144 1869-6104 |
| DOI: | 10.1515/gcc-2019-2007⟩ |
| Popis: | Garside-theoretical solutions to the conjugacy problem in braid groups depend on the determination of a characteristic subset of the conjugacy class of any given braid, e.g. the sliding circuit set. It is conjectured that, among rigid braids with a fixed number of strands, the size of this set is bounded by a polynomial in the length of the braids. In this paper we suggest a more precise bound: for rigid braids with $N$ strands and of Garside length $L$, the sliding circuit set should have at most $C\cdot L^{N-2}$ elements, for some constant $C$. We construct a family of braids which realise this potential worst case. Our example braids suggest that having a large sliding circuit set is a geometric property of braids, as our examples have multiple subsurfaces with large subsurface projection; thus they are "almost reducible" in multiple ways, and act on the curve graph with small translation distance. 4 figures |
| Databáze: | OpenAIRE |
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