Categorifying the Knizhnik-Zamolodchikov connection

DOI10.1016/j.difgeo.2012.03.004zbMath1270.53077arXiv1106.0042OpenAlexW2122068783WikidataQ59902450 ScholiaQ59902450MaRDI QIDQ428917

João Faria Martins, Lucio Simone Cirio

Publication date: 25 June 2012

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.0042

zbMATH Keywords

higher gauge theorychord diagrams4-term relationbraided surfacecategorical representationdifferential crossed moduleinfinitesimal braidingKnizhnik-Zamolodchikov equationstwo-dimensional holonomy

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Braid groups; Artin groups (20F36) Issues of holonomy in differential geometry (53C29) Yang-Baxter equations (16T25)

Related Items

Formal connections, higher holonomy functors and iterated integrals, A Kontsevich integral of order 1, Crossed modules of Hopf algebras and of associative algebras and two-dimensional holonomy, Higher holonomy maps for hyperplane arrangements, Holonomies of gauge fields in twistor space 6: Incorporation of massive fermions, Infinitesimal 2-braidings and differential crossed modules

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The fundamental Gray 3-groupoid of a smooth manifold and local 3-dimensional holonomy based on a 2-crossed module
• Smooth functors vs. differential forms
• Surface holonomy for non-Abelian 2-bundles via double groupoids
• An invitation to higher gauge theory
• Monodromy representations of braid groups and Yang-Baxter equations
• Current algebras and Wess-Zumino model in two dimensions
• Quantum field theory and the Jones polynomial
• Groupoids and crossed objects in algebraic topology
• Lectures on algebraic topology.
• The cohomology ring of the colored braid group
• 2-groupoid enrichments in homotopy theory and algebra
• On the Vassiliev knot invariants
• Holonomy and parallel transport for abelian gerbes
• Surfaces in 4-space
• On universal Vassiliev invariants
• Representation of the category of tangles by Kontsevich's iterated integral
• Representation theory of 2-groups on Kapranov and Voevodsky's 2-vector spaces
• Braid cobordisms, triangulated categories, and flag varieties
• From loop groups to 2-groups
• On the deformation of rings and algebras. II
• Iterated integrals of differential forms and loop space homology
• Differential geometry of gerbes
• Theory of braids
• Cohomology theory in abstract groups. III. Operator homomorphisms of kernels
• Connections on non-abelian Gerbes and their Holonomy
• Principal 2-bundles and their gauge 2-groups
• On two-dimensional holonomy
• The fundamental crossed module of the complement of a knotted surface
• Higher gauge theory—differential versus integral formulation
• On Lie Algebra Crossed Modules