Search results for "Vassiliev Invariant"

showing 2 items of 2 documents

Vassiliev invariants for braids on surfaces

2000

We show that Vassiliev invariants separate braids on a closed oriented surface, and we exhibit an universal Vassiliev invariant for these braids in terms of chord diagrams labeled by elements of the fundamental group of the considered surface.

Surface (mathematics)Fundamental groupLow-dimensional topologyGeneral MathematicsBraid groupGroup Theory (math.GR)braidMathematics::Algebraic TopologyCombinatoricsMathematics - Geometric TopologyMathematics::Group TheoryMathematics::Category TheoryMathematics::Quantum Algebra20F36 (Primary) 57M2757N05 (Secondary)BraidFOS: MathematicssurfaceMathematicsApplied MathematicsGeometric Topology (math.GT)Mathematics::Geometric TopologyFinite type invariantVassiliev Invariantfinite type invariantIsomorphismMathematics - Group TheoryGroup theory
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Compressed Drinfeld associators

2004

Drinfeld associator is a key tool in computing the Kontsevich integral of knots. A Drinfeld associator is a series in two non-commuting variables, satisfying highly complicated algebraic equations - hexagon and pentagon. The logarithm of a Drinfeld associator lives in the Lie algbera L generated by the symbols a,b,c modulo [a,b]=[b,c]=[c,a]. The main result is a description of compressed associators that satisfy the compressed pentagon and hexagon in the quotient L/[[L,L],[L,L]]. The key ingredient is an explicit form of Campbell-Baker-Hausdorff formula in the case when all commutators commute.

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Hexagon equationPure mathematicsCampbell–Baker–Hausdorff formulaKnotLie algebraModuloCompressed Vassiliev invariantsPentagon equation01 natural sciencessymbols.namesakeMathematics - Geometric TopologyChord diagramsExtended Bernoulli numbers[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]Mathematics::Quantum Algebra0103 physical sciencesLie algebraMathematics - Quantum AlgebraFOS: MathematicsQuantum Algebra (math.QA)0101 mathematicsAlgebraic numberBernoulli numberQuotientMathematics[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]Zeta functionDiscrete mathematics[MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA]Algebra and Number TheoryVassiliev invariants[ MATH.MATH-QA ] Mathematics [math]/Quantum Algebra [math.QA]Drinfeld associator57M25 57M27 11B68 17B01010102 general mathematicsAssociatorQuantum algebraGeometric Topology (math.GT)Kontsevich integralRiemann zeta functionsymbols[MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA]Compressed associator010307 mathematical physicsBernoulli numbers
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