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 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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology 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
   • CommentTimeMay 2nd 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexPage created, but author did not leave any comments. <a href="https://ncatlab.org/nlab/revision/tesselation/1">v1</a>, <a href="https://ncatlab.org/nlab/show/tesselation">current</a>

   Page created, but author did not leave any comments.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 4th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded some basic words to the Idea-section <a href="https://ncatlab.org/nlab/revision/diff/tesselation/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/tesselation/2">v2</a>, <a href="https://ncatlab.org/nlab/show/tesselation">current</a>

   added some basic words to the Idea-section

   diff, v2, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 14th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexI am still looking to understand the combinatorial rule -- if any -- which for a given type of hyperbolic tesselation constructs the corresponding chord diagram -- if any -- stage-wise. One can see the first three such stages for the the $\{5,4\}$ tessalation in [this Fig 6.](https://arxiv.org/pdf/1911.03485.pdf#page=8). Apparently these authors use an algoirthm called "vertex inflation", apparently due to [arXiv:1805.02665](https://arxiv.org/abs/1805.02665). So I guess I know one place where to look now. But I still feel that the rule "Schlaefli symbol $\mapsto$ chord diagram" that I am after must be something nice and simple that is known in the maths literature? <a href="https://ncatlab.org/nlab/revision/diff/tesselation/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/tesselation/7">v7</a>, <a href="https://ncatlab.org/nlab/show/tesselation">current</a>

   I am still looking to understand the combinatorial rule – if any – which for a given type of hyperbolic tesselation constructs the corresponding chord diagram – if any – stage-wise.

   One can see the first three such stages for the the $\{5,4\}$ tessalation in this Fig 6.. Apparently these authors use an algoirthm called “vertex inflation”, apparently due to arXiv:1805.02665.

   So I guess I know one place where to look now. But I still feel that the rule “Schlaefli symbol $\mapsto$ chord diagram” that I am after must be something nice and simple that is known in the maths literature?

   diff, v7, current