Quantum Groups and Knot Theory: Week
ثبت نشده
چکیده
One of the most important applications of the RT-functor is the construction of invariants of (closed, connected, oriented) 3-manifolds, the so-called Reshetikhin-Turaev-Witten invariants of 3-manifolds. However, the RT-invariants of ribbon links associated with colorings of links with objects of a ribbon category C in week 46 and week 47 are far too general for this purpose. For this more ambitious goal we are forced to impose a very restrictive additional property of the ribbon category C turning it into a so-called modular tensor category.
منابع مشابه
Quantum Groups and Knot Theory Lecture: Week
This week in class we treat quantum traces and dimensions in general ribbon categories (from the syllabus of week 46, see also [2, Chapter 6]) and we define the general notion of ribbon algebras and discuss how these give rise relation to ribbon categories. This material will be used in later to give some important explicit constructions of ribbon categories. The syllabus of this week 47 contai...
متن کاملFrom 3-moves to Lagrangian tangles and cubic skein modules
We present an expanded version of four talks describing recent developments in Knot Theory to which the author contributed. We discuss several open problems in classical Knot Theory and we develop techniques that allow us to study them: Lagrangian tangles, skein modules and Burnside groups. The method of Burnside groups of links was discovered and developed only half a year after the last talk ...
متن کاملof Knot Theory and Its Ramifications
We give a diagrammatic definition of Uq(sl2) when q is not a root of unity, including the Hopf algebra structure and relationship with the Temperley-Lieb category. Quantum groups, knot diagrams, skein theory.
متن کاملLogarithmic Knot Invariants Arising from Restricted Quantum Groups
We construct knot invariants from the radical part of projective modules of the restricted quantum group Uq(sl2) at q = exp(π √ −1/p), and we also show a relation between these invariants and the colored Alexander invariants. These projective modules are related to logarithmic conformal field theories.
متن کاملKnot Invariants and New Quantum Field Theory
We propose a new gauge theory of quantum electrodynamics (QED) and quantum chromodynamics (QCD) from which we derive knot invariants such as the Jones polynomial. Our approach is inspired by the work of Witten who derived knot invariants from quantum field theory based on the Chern-Simon Lagrangian. From our approach we can derive new knot invariants which extend the Jones polynomial and give a...
متن کامل