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 کاملAxioms for Hopf Invariants
1. Since H. Hopf first proved that irziS) « Z by showing that a certain invariant was non tri vial, several similar invariants—called generalized Hopf invariants—have been described; indeed, there are no less than 6 different definitions in the literature, and it was not always clear whether theorems about one applied to others. Many definitions were riddled with choices which had to be made, a...
متن کاملInvariants of Hopf Algebras
In the winter of 1999 I gave a series of lectures at Queen’s university about some recent results concerning the Cohen-Macaulay property of invariants of Hopf algebras. Tony Geramita asked me to write up my notes for the Queen’s Papers, and I happily took up his suggestion. Although this article focuses on the proof of one main theorem (Theorem 2.11 on page 12), it has some of the character of ...
متن کاملVassiliev Invariants, Chord Diagrams, and Jacobi Diagrams
The goal of this paper is to understand the topological meaning of Jacobi diagrams in relation to knot theory and finite type knot invariants, otherwise known as Vassiliev invariants. To do so, we will first set up the notions of: the Vassiliev invariant and its respective space, the space of chord diagrams, a weight system on chord diagrams, and Jacobi diagrams and their respective space. Duri...
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 §...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2005
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2005.5.1677