100, rue des maths 38610 Gières / GPS : 45.193055, 5.772076 / Directeur : Louis Funar

How an ordinary Hopf algebra yields a 3-manifold invariant

Vendredi, 12 Novembre, 2010 - 11:30
Prénom de l'orateur : 
Greg
Nom de l'orateur : 
Kuperberg
Résumé : 

There are many constructions of quantum 3-manifold invariants, some of them complicated and some of them not so complicated. I will describe a relatively less popular invariant of 3-manifolds whose definition and proof of invariance is among the simplest in the field of quantum algebra. Given a 3-manifold M and a finite-dimensional Hopf algebra H, a Heegaard diagram for M can be read as a scalar-valued word in the structure tensors of H. Objects such as R-matrices, associators, or representation categories are not needed in the construction.

If time permits, I will discuss a converse result: The formal word problem for finite, involutory Hopf objects can be solved using 3-manifold topology.

Institution de l'orateur : 
UC Davis & Institut Fourier
Thème de recherche : 
Topologie
Salle : 
04
logo uga logo cnrs