Search results for " Braid group"

showing 4 items of 4 documents

Hurwitz spaces of Galois coverings of P^1, whose Galois groups are Weyl groups

2006

We prove the irreducibility of the Hurwitz spaces which parametrize Galois coverings of P^1 whose Galois group is an arbitrary Weyl group and the local monodromies are reflections. This generalizes a classical theorem due to Clebsch and Hurwitz.

Hurwitz space Weyl group Braid group
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Irreducible components of Hurwitz spaces parameterizing Galois coverings of curves of positive genus

2014

Let Y be a smooth, projective, irreducible complex curve. A G-covering p : C → Y is a Galois covering, where C is a smooth, projective, irreducible curve and an isomorphism G ∼ −→ Aut(C/Y ) is fixed. Two G-coverings are equivalent if there is a G-equivariant isomorphism between them. We are concerned with the Hurwitz spaces H n (Y ) and H G n (Y, y0). The first one parameterizes Gequivalence classes of G-coverings of Y branched in n points. The second one, given a point y0 ∈ Y , parameterizes G-equivalence classes of pairs [p : C → Y, z0], where p : C → Y is a G-covering unramified at y0 and z0 ∈ p (y0). When G = Sd one can equivalently consider coverings f : X → Y of degree d with full mon…

Discrete mathematicsHurwitz quaternionHurwitz space Galois covering Braid groupGalois cohomologyInverse Galois problemGeneral MathematicsGalois groupSplitting of prime ideals in Galois extensionsEmbedding problemCombinatoricsHurwitz's automorphisms theoremGalois extensionSettore MAT/03 - GeometriaMathematics
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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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Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups

2003

We prove by explicit construction that graph braid groups and most surface groups can be embedded in a natural way in right-angled Artin groups, and we point out some consequences of these embedding results. We also show that every right-angled Artin group can be embedded in a pure surface braid group. On the other hand, by generalising to right-angled Artin groups a result of Lyndon for free groups, we show that the Euler characteristic -1 surface group (given by the relation x^2y^2=z^2) never embeds in a right-angled Artin group.

graph groupBraid group20F36Group Theory (math.GR)Graphright-angled Artin groupCombinatorics20F36 05C25 05C25symbols.namesakeMathematics::Group Theory05C25Euler characteristicFOS: MathematicssymbolsBraidEmbeddingArtin groupGeometry and Topologygraph braid groupMathematics - Group Theoryconfiguration spacecubed complexMathematics
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