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
   • CommentTimeJan 6th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexstarting something -- not done yet, but need to save <a href="https://ncatlab.org/nlab/revision/%27t+Hooft+double+line+notation/1">v1</a>, <a href="https://ncatlab.org/nlab/show/%27t+Hooft+double+line+notation">current</a>

   starting something – not done yet, but need to save

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJan 6th 2020
   • (edited Jan 6th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexnow some substance in place, including various graphics. **Question:** Did anybody else notice/make explicit in print that Bar-Natan's discussion of marked surfaces in relation to Lie algebra weight systems (section 6 in [Bar-Natan 95](https://ncatlab.org/nlab/show/'t+Hooft+double+line+notation#BarNatan95)) is exactly the 't Hooft double line construction for $\mathfrak{so}(N)$? <a href="https://ncatlab.org/nlab/revision/%27t+Hooft+double+line+notation/1">v1</a>, <a href="https://ncatlab.org/nlab/show/%27t+Hooft+double+line+notation">current</a>

   now some substance in place, including various graphics.

   Question: Did anybody else notice/make explicit in print that Bar-Natan’s discussion of marked surfaces in relation to Lie algebra weight systems (section 6 in Bar-Natan 95) is exactly the ’t Hooft double line construction for $\mathfrak{so}(N)$?

   v1, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJan 7th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded another early reference on the case of $SO(N)$ and $Sp(N)$: * G.M. Cicuta, _Topological Expansion for $SO(N)$ and $Sp(2n)$ Gauge Theories_, Lett. Nuovo Cim. 35 (1982) 87 ([spire:177713](http://inspirehep.net/record/177713), [doi:10.1007/BF02754653](https://doi.org/10.1007/BF02754653)) <a href="https://ncatlab.org/nlab/revision/diff/%27t+Hooft+double+line+notation/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/%27t+Hooft+double+line+notation/4">v4</a>, <a href="https://ncatlab.org/nlab/show/%27t+Hooft+double+line+notation">current</a>

   added another early reference on the case of $SO(N)$ and $Sp(N)$:

   • G.M. Cicuta, Topological Expansion for $SO(N)$ and $Sp(2n)$ Gauge Theories, Lett. Nuovo Cim. 35 (1982) 87 (spire:177713, doi:10.1007/BF02754653)

   diff, v4, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJan 8th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a graphics with an actual example before passing to surfaces ([here](https://ncatlab.org/nlab/show/'t+Hooft+double+line+notation#Example)) <a href="https://ncatlab.org/nlab/revision/diff/%27t+Hooft+double+line+notation/12">diff</a>, <a href="https://ncatlab.org/nlab/revision/%27t+Hooft+double+line+notation/12">v12</a>, <a href="https://ncatlab.org/nlab/show/%27t+Hooft+double+line+notation">current</a>

   added a graphics with an actual example before passing to surfaces (here)

   diff, v12, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJan 8th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded another example of the surface-valued construction ([here](https://ncatlab.org/nlab/show/'t+Hooft+double+line+notation#SurfaceExample)) <a href="https://ncatlab.org/nlab/revision/diff/%27t+Hooft+double+line+notation/13">diff</a>, <a href="https://ncatlab.org/nlab/revision/%27t+Hooft+double+line+notation/13">v13</a>, <a href="https://ncatlab.org/nlab/show/%27t+Hooft+double+line+notation">current</a>

   added another example of the surface-valued construction (here)

   diff, v13, current