Search results for "Artin groups"

showing 5 items of 5 documents

Automorphisms of 2–dimensional right-angled Artin groups

2007

We study the outer automorphism group of a right-angled Artin group AA in the case where the defining graph A is connected and triangle-free. We give an algebraic description of Out.AA/ in terms of maximal join subgraphs in A and prove that the Tits’ alternative holds for Out.AA/. We construct an analogue of outer space for Out.AA/ and prove that it is finite dimensional, contractible, and has a proper action of Out.AA/. We show that Out.AA/ has finite virtual cohomological dimension, give upper and lower bounds on this dimension and construct a spine for outer space realizing the most general upper bound. 20F36; 20F65, 20F28

20F36outer spaceCohomological dimensionComputer Science::Digital LibrariesQuantitative Biology::Other01 natural sciencesContractible spaceUpper and lower boundsCombinatorics0103 physical sciences20F650101 mathematicsAlgebraic numberMathematics20F28Quantitative Biology::Biomolecules010102 general mathematicsAstrophysics::Instrumentation and Methods for AstrophysicsOuter automorphism groupAutomorphismGraphArtin groupright-angled Artin groups010307 mathematical physicsGeometry and Topologyouter automorphismsGeometry & Topology
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Conjugacy problem for braid groups and Garside groups

2003

We present a new algorithm to solve the conjugacy problem in Artin braid groups, which is faster than the one presented by Birman, Ko and Lee. This algorithm can be applied not only to braid groups, but to all Garside groups (which include finite type Artin groups and torus knot groups among others).

Conjugacy problemBraid group20F36Geometric topologyGarside groupsGroup Theory (math.GR)0102 computer and information sciencesAlgebraic topology01 natural sciencesTorus knotCombinatoricsMathematics - Geometric TopologyMathematics::Group TheoryMathematics::Quantum AlgebraFOS: MathematicsAlgebraic Topology (math.AT)Mathematics - Algebraic Topology0101 mathematics20F36; 20F10MathematicsSmall Gaussian groupsAlgebra and Number Theory010102 general mathematicsConjugacy problemBraid groupsGeometric Topology (math.GT)Braid theoryMathematics::Geometric TopologyArtin groups010201 computation theory & mathematicsArtin group20F10Mathematics - Group TheoryGroup theory
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Ordering Garside groups

2017

We introduce a condition on Garside groups that we call Dehornoy structure. An iteration of such a structure leads to a left order on the group. We show conditions for a Garside group to admit a Dehornoy structure, and we apply these criteria to prove that the Artin groups of type A and I2(m), m ≥ 4, have Dehornoy structures. We show that the left orders on the Artin groups of type A obtained from their Dehornoy structures are the Dehornoy orders. In the case of the Artin groups of type I2(m), m ≥ 4, we show that the left orders derived from their Dehornoy structures coincide with the orders obtained from embeddings of the groups into braid groups.

Garside TheoryThéorie de GarsideOrderable GroupsGroupes d'ArtinGroupes OrdonnablesArtin Groups[MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]
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The HOMFLY-PT polynomials of sublinks and the Yokonuma–Hecke algebras

2016

We describe completely the link invariants constructed using Markov traces on the Yokonuma-Hecke algebras in terms of the linking matrix and the HOMFLYPT polynomials of sublinks.

MSC: Primary 57M27: Invariants of knots and 3-manifolds Secondary 20C08: Hecke algebras and their representations 20F36: Braid groups; Artin groups 57M25: Knots and links in $S^3$Pure mathematicsMarkov chainGeneral Mathematics010102 general mathematicsYokonuma-Hecke algebrasGeometric Topology (math.GT)Linking numbers01 natural sciencesMathematics::Geometric TopologyMatrix (mathematics)Mathematics - Geometric TopologyMarkov tracesMathematics::Quantum Algebra[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesMathematics - Quantum AlgebraFOS: MathematicsQuantum Algebra (math.QA)010307 mathematical physics0101 mathematicsRepresentation Theory (math.RT)Link (knot theory)Mathematics - Representation TheoryMathematics
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Presentations for the punctured mapping class groups in terms of Artin groups

1999

Consider an oriented compact surface F of positive genus, possibly with boundary, and a finite set P of punctures in the interior of F, and define the punctured mapping class group of F relatively to P to be the group of isotopy classes of orientation-preserving homeomorphisms h: F-->F which pointwise fix the boundary of F and such that h(P) = P. In this paper, we calculate presentations for all punctured mapping class groups. More precisely, we show that these groups are isomorphic with quotients of Artin groups by some relations involving fundamental elements of parabolic subgroups.

Pointwise20F38Class (set theory)presentationsGroup (mathematics)20F36Boundary (topology)Geometric Topology (math.GT)mapping class groupsSurface (topology)Mathematics::Geometric TopologyMapping class groupCombinatoricsMathematics - Geometric TopologyArtin groupsGenus (mathematics)FOS: MathematicsIsotopyGeometry and Topology57N0557N05 20F36 20F38MathematicsAlgebraic & Geometric Topology
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