Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeDec 26th 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a bunch of references <a href="https://ncatlab.org/nlab/revision/diff/Kontsevich+integral/6">diff</a>, <a href="https://ncatlab.org/nlab/revision/Kontsevich+integral/6">v6</a>, <a href="https://ncatlab.org/nlab/show/Kontsevich+integral">current</a>

   added a bunch of references

   diff, v6, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJan 9th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to this review: * Christine Lescop, _Introduction to the Kontsevich Integral of Framed Tangles_, 2000 ([[LescopKontsevichIntegral.pdf:file]]) <a href="https://ncatlab.org/nlab/revision/diff/Kontsevich+integral/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/Kontsevich+integral/7">v7</a>, <a href="https://ncatlab.org/nlab/show/Kontsevich+integral">current</a>

   added pointer to this review:

   • Christine Lescop, Introduction to the Kontsevich Integral of Framed Tangles, 2000 (LescopKontsevichIntegral.pdf:file)

   diff, v7, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJan 12th 2020
   • (edited Jan 12th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexThe Kontsevich integral is a rather beautiful and canonical beast: it's "just" the Dyson formula for the holonomy of the Knizhnik-Zamolodchikov connection. The latter, in turn, is itself rather beautiful in its universal form with values in horizontal chord diagrams. This nice state of affairs didn't really come across in what we had in the entry. In an attempt to begin to improve on this, I have started a new subsection _[Definition -- On braids](https://ncatlab.org/nlab/show/Kontsevich+integral#OnBraids)_. The previous material is currently still there under _[Definition -- On knots](https://ncatlab.org/nlab/show/Kontsevich+integral#OnKnots)_, but I hope to adjust and streamline this. Since these core definitions really belong to several entries, such as also to _[[Knizhnik-Zamolodchikov connection]]_, _[[braid representation]]_ and _[[configuration space of points]]_, I'll give it a bare entry * _[[Knizhnik-Zamolodchikov-Kontsevich construction -- definition]]_ to be `!include`-ed into these related entries <a href="https://ncatlab.org/nlab/revision/diff/Kontsevich+integral/8">diff</a>, <a href="https://ncatlab.org/nlab/revision/Kontsevich+integral/8">v8</a>, <a href="https://ncatlab.org/nlab/show/Kontsevich+integral">current</a>

   The Kontsevich integral is a rather beautiful and canonical beast: it’s “just” the Dyson formula for the holonomy of the Knizhnik-Zamolodchikov connection. The latter, in turn, is itself rather beautiful in its universal form with values in horizontal chord diagrams.

   This nice state of affairs didn’t really come across in what we had in the entry. In an attempt to begin to improve on this, I have started a new subsection Definition – On braids.

   The previous material is currently still there under Definition – On knots, but I hope to adjust and streamline this.

   Since these core definitions really belong to several entries, such as also to Knizhnik-Zamolodchikov connection, braid representation and configuration space of points, I’ll give it a bare entry

   • Knizhnik-Zamolodchikov-Kontsevich construction – definition

   to be !include-ed into these related entries

   diff, v8, current