منابع مشابه
Hopf diagrams and quantum invariants
The Reshetikhin-Turaev invariant, Turaev’s TQFT, and many related constructions rely on the encoding of certain tangles (n-string links, or ribbon n-handles) as n-forms on the coend of a ribbon category. We introduce the monoidal category of Hopf diagrams, and describe a universal encoding of ribbon string links as Hopf diagrams. This universal encoding is an injective monoidal functor and admi...
متن کاملHopf Algebras of Diagrams
G. H. E. DUCHAMP∗,§, J.-G. LUQUE†,¶, J.-C. NOVELLI‡,‖, C. TOLLU∗,∗∗ and F. TOUMAZET‡,†† ∗Institut Galilée, LIPN, CNRS UMR 7030 99, Avenue J.-B. Clement, F-93430 Villetaneuse, France †LITIS, Université de Rouen; Avenue de l’université 76801 Saint Étienne du Rouvray, France ‡Université Paris-Est, Institut Gaspard Monge 5 Boulevard Descartes, Champs-Sur-Marne 77454 Marne-la-Vallée Cedex 2 France §...
متن کاملThe Plumbing of Minimal Area Surfaces
⋆ Partially supported by the National Science Foundation; Alfred P. Sloan Research Fellow. † Permanent address: Center for Theoretical Physics, MIT, Cambridge, Mass. 02139. Supported in part D.O.E. contract DE-AC02-76ER03069 and NSF grant PHY91-06210. We study the metric of minimal area on a punctured Riemann surface under the condition that all nontrivial homotopy closed curves be longer than ...
متن کاملHopf Algebras on Decorated Noncrossing Arc Diagrams
Noncrossing arc diagrams are combinatorial models for the equivalence classes of the lattice congruences of the weak order on permutations. In this paper, we provide a general method to endow these objects with Hopf algebra structures. Specific instances of this method produce relevant Hopf algebras that appeared earlier in the literature.
متن کاملMinimal Area Nonorientable String Diagrams
We use minimal area metrics to generate all nonorientable string diagrams. The surfaces in unoriented string theory have nontrivial open curves and nontrivial closed curves whose neighborhoods are either annuli or Möbius strips. We define a minimal area problem by imposing length conditions on open curves and on annular closed curves only. We verify that the minimal area conditions are respecte...
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ژورنال
عنوان ژورنال: Commentarii Mathematici Helvetici
سال: 2005
ISSN: 0010-2571
DOI: 10.4171/cmh/28