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 nlab noncommutative noncommutative-geometry number-theory object 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 23rd 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexsome minimum <a href="https://ncatlab.org/nlab/revision/loop+braid+group/1">v1</a>, <a href="https://ncatlab.org/nlab/show/loop+braid+group">current</a>

   some minimum

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 23rd 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded full publication data for: * [[Xiao-Song Lin]], *The motion group of the unlink and its representations*, in: *Xiao-Song Lin's Unpublished Papers* ([doi:10.1142/9789812819116_others01](https://doi.org/10.1142/9789812819116_others01)), Part B of: [[Kevin Lin]], [[Zhenghan Wang]], [[Weiping Zhang]] (eds.) *Topology and Physics: Proceedings of the Nankai International Conference in Memory of Xiao-Song Lin*, Tianjin, China, 27-31 July 2007. World Scientific, 2008 ([doi:10.1142/6907](https://doi.org/10.1142/6907)) but in the end there is still no electronic copy of the article. <a href="https://ncatlab.org/nlab/revision/diff/loop+braid+group/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/loop+braid+group/2">v2</a>, <a href="https://ncatlab.org/nlab/show/loop+braid+group">current</a>

   added full publication data for:

   • Xiao-Song Lin, The motion group of the unlink and its representations, in:

     Xiao-Song Lin’s Unpublished Papers (doi:10.1142/9789812819116_others01), Part B of:

     Kevin Lin, Zhenghan Wang, Weiping Zhang (eds.) Topology and Physics: Proceedings of the Nankai International Conference in Memory of Xiao-Song Lin, Tianjin, China, 27-31 July 2007. World Scientific, 2008 (doi:10.1142/6907)

   but in the end there is still no electronic copy of the article.

   diff, v2, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 7th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Chenjie Wang]], [[Michael Levin]], *Braiding Statistics of Loop Excitations in Three Dimensions*, Phys. Rev. Lett. **113** (2014) 080403 ([doi:10.1103/PhysRevLett.113.080403](https://doi.org/10.1103/PhysRevLett.113.080403)) <a href="https://ncatlab.org/nlab/revision/diff/loop+braid+group/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/loop+braid+group/4">v4</a>, <a href="https://ncatlab.org/nlab/show/loop+braid+group">current</a>

   added pointer to:

   • Chenjie Wang, Michael Levin, Braiding Statistics of Loop Excitations in Three Dimensions, Phys. Rev. Lett. 113 (2014) 080403 (doi:10.1103/PhysRevLett.113.080403)

   diff, v4, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeMay 7th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexand to: * Chao-Ming Jian, Xiao-Liang Qi, *Layer Construction of 3D Topological States and String Braiding Statistics*, Phys. Rev. X **4** (2014) 041043 $[$[doi:10.1103/PhysRevX.4.041043](https://doi.org/10.1103/PhysRevX.4.041043)$]$ <a href="https://ncatlab.org/nlab/revision/diff/loop+braid+group/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/loop+braid+group/4">v4</a>, <a href="https://ncatlab.org/nlab/show/loop+braid+group">current</a>

   and to:

   • Chao-Ming Jian, Xiao-Liang Qi, Layer Construction of 3D Topological States and String Braiding Statistics, Phys. Rev. X 4 (2014) 041043 $[$doi:10.1103/PhysRevX.4.041043$]$

   diff, v4, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeAug 22nd 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to today's * Zhi-Feng Zhang, Qing-Rui Wang, [[Peng Ye]], *Wilson Operators, Non-Abelian Fusion Rules, and Loop Shrinking Rules of Borromean Rings Topological Order* &lbrack;[arXiv:2208.09228](https://arxiv.org/abs/2208.09228)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/loop+braid+group/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/loop+braid+group/5">v5</a>, <a href="https://ncatlab.org/nlab/show/loop+braid+group">current</a>

   added pointer to today’s

   • Zhi-Feng Zhang, Qing-Rui Wang, Peng Ye, Wilson Operators, Non-Abelian Fusion Rules, and Loop Shrinking Rules of Borromean Rings Topological Order [arXiv:2208.09228]

   diff, v5, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeOct 25th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to today's: * Pramod Padmanabhan, Abhishek Chowdhury, *Loop braid groups and integrable models* &lbrack;[arXiv:2210.12932](https://arxiv.org/abs/2210.12932)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/loop+braid+group/6">diff</a>, <a href="https://ncatlab.org/nlab/revision/loop+braid+group/6">v6</a>, <a href="https://ncatlab.org/nlab/show/loop+braid+group">current</a>

   added pointer to today’s:

   • Pramod Padmanabhan, Abhishek Chowdhury, Loop braid groups and integrable models [arXiv:2210.12932]

   diff, v6, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeDec 6th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexWe ought to have a dedicated page for "[[motion group]]". That not existing yet, for the moment I am recording the following reference here: * [[Fiona Torzewska]], [[João Faria Martins]], [[Paul Purdon Martin]], *Motion groupoids and mapping class groupoids*, Comm. Math. Phys. **402** (2023) 1621-1705 &lbrack;[arXiv:2103.10377](https://arxiv.org/abs/2103.10377), [doi:10.1007/s00220-023-04755-0](https://doi.org/10.1007/s00220-023-04755-0)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/loop+braid+group/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/loop+braid+group/7">v7</a>, <a href="https://ncatlab.org/nlab/show/loop+braid+group">current</a>

   We ought to have a dedicated page for “motion group”. That not existing yet, for the moment I am recording the following reference here:

   • Fiona Torzewska, João Faria Martins, Paul Purdon Martin, Motion groupoids and mapping class groupoids, Comm. Math. Phys. 402 (2023) 1621-1705 [arXiv:2103.10377, doi:10.1007/s00220-023-04755-0]

   diff, v7, current

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeDec 12th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * Celeste Damiani, *A journey through loop braid groups*, Expositiones Mathematicae **35** 3 (2017) 252-285 &lbrack;[doi:10.1016/j.exmath.2016.12.003](https://doi.org/10.1016/j.exmath.2016.12.003)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/loop+braid+group/8">diff</a>, <a href="https://ncatlab.org/nlab/revision/loop+braid+group/8">v8</a>, <a href="https://ncatlab.org/nlab/show/loop+braid+group">current</a>

   added pointer to:

   • Celeste Damiani, A journey through loop braid groups, Expositiones Mathematicae 35 3 (2017) 252-285 [doi:10.1016/j.exmath.2016.12.003]

   diff, v8, current