Links, Quantum Groups and Tqfts
نویسنده
چکیده
X iv :q -a lg /9 50 60 02 v2 3 1 Ju l 1 99 5 Abstract. The Jones polynomial and the Kauffman bracket are constructed, and their relation with knot and link theory is described. The quantum groups and tangle functor formalisms for understanding these invariants and their descendents are given. The quantum group Uq(sl2), which gives rise to the Jones polynomial, is constructed explicitly. The 3-manifold invariants and the axiomatic topological quantum field theories which arise from these link invariants at certain values of the parameter are constructed.
منابع مشابه
Jones-witten Invariants for Nonsimply-connected Lie Groups and the Geometry of the Weyl Alcove
The quotient process of Müger and Bruguières is used to construct modular categories and TQFTs out of closed subsets of the Weyl alcove of a simple Lie algebra. In particular it is determined at which levels closed subsets associated to nonsimplyconnected groups lead to TQFTs. Many of these TQFTs are shown to decompose into a tensor product of TQFTs coming from smaller subsets. The “prime” subs...
متن کامل0 O ct 2 00 7 ON EXOTIC MODULAR TENSOR CATEGORIES
It has been conjectured that every (2+1)-TQFT is a Chern-SimonsWitten (CSW) theory labelled by a pair (G, λ), where G is a compact Lie group, and λ ∈ H(BG;Z) a cohomology class. We study two TQFTs constructed from Jones’ subfactor theory which are believed to be counterexamples to this conjecture: one is the quantum double of the even sectors of the E6 subfactor, and the other is the quantum do...
متن کامل0 Ju n 20 08 ON EXOTIC MODULAR TENSOR CATEGORIES
It has been conjectured that every (2+1)-TQFT is a Chern-SimonsWitten (CSW) theory labeled by a pair (G, λ), where G is a compact Lie group, and λ ∈ H(BG;Z) a cohomology class. We study two TQFTs constructed from Jones’ subfactor theory which are believed to be counterexamples to this conjecture: one is the quantum double of the even sectors of the E6 subfactor, and the other is the quantum dou...
متن کاملar X iv : 0 71 0 . 57 61 v 2 [ m at h . G T ] 8 N ov 2 00 7 ON EXOTIC MODULAR TENSOR CATEGORIES
It has been conjectured that every (2+1)-TQFT is a Chern-SimonsWitten (CSW) theory labelled by a pair (G, λ), where G is a compact Lie group, and λ ∈ H(BG;Z) a cohomology class. We study two TQFTs constructed from Jones’ subfactor theory which are believed to be counterexamples to this conjecture: one is the quantum double of the even sectors of the E6 subfactor, and the other is the quantum do...
متن کاملOpen-closed TQFTs extend Khovanov homology from links to tangles
We use a special kind of 2-dimensional extended Topological Quantum Field Theories (TQFTs), so-called open-closed TQFTs, in order to extend Khovanov homology from links to arbitrary tangles, not necessarily even. For every plane diagram of an oriented tangle, we construct a chain complex whose homology is invariant under Reidemeister moves. The terms of this chain complex are modules of a suita...
متن کامل