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Thick tangles

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1765)

Abstract

It is a rather involved task to describe the relations between isomorphisms between various functors which use coends. To make them accessible we introduce the monoidal bicategory of thick tangles as a kind of a free monoidal bicategory with duals generated by a self-dual object. An analogy would be to introduce the category of unoriented tangles as the free braided category, generated by a self-dual object. Naturally, the bicategory of thick tangles is much simpler than its braided counterpart— the category of 2-tangles proposed by Baez and Langford [BL98a]. They prove in [BL98b] that the category of 2-tangles is a free semistrict braided monoidal 2-category with duals on one unframed self-dual object. Very similar geometric 2-categories appear in the theory of knotted surfaces in 4-dim space as developed by Carter, Saito, Fischer, and others, see for example [CRS97], [CS98], and [Fi94].

Keywords

  • Planar Graph
  • Monoidal Category
  • Abelian Category
  • Isotopy Class
  • Identity Morphism

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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(2001). Thick tangles. In: Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners. Lecture Notes in Mathematics, vol 1765. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44625-7_11

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