%!TEX root = ../article.tex \title{\hspace{-0.95cm}Knot polynomial identities and quantum group coincidences} \newcommand{\Primaryclass}[1]{\primaryclass{#1}} \newcommand{\Secondaryclass}[1]{\secondaryclass{#1}} \newcommand{\Keywords}[1]{\keywords{#1}} \newcommand{\Author}[2]{\author{#1}\email{#2}} \author{Scott~Morrison}\email{scott@tqft.net} \author{Emily~Peters}\email{eep@euclid.unh.edu} \author{Noah~Snyder}\email{nsnyder@math.columbia.edu} \address{% \rm URLs:\stdspace \tt \url{http://tqft.net/}\ \ \url{http://euclid.unh.edu/~eep}\\\rm and \tt \url{http://math.columbia.edu/~nsnyder}} \Primaryclass{ %18 %Category theory; homological algebra %18D %Categories with structure 18D10 %Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23] } \Secondaryclass{ 57M27 %Invariants of knots and 3-manifolds %17 %Nonassociative rings and algebras %17B %Lie algebras and Lie superalgebras [For Lie groups, see 22Exx] 17B10 %Representations, algebraic theory (weights) %81 %Quantum theory %81R %Groups and algebras in quantum theory 81R05 %Finite-dimensional groups and algebras motivated by physics and their representations [See also 20C35, 22E70] %57 %Manifolds and cell complexes [For complex manifolds, see 32Qxx] %57R %Differential topology [For foundational questions of differentiable manifolds, see 58Axx; for infinite-dimensional manifolds, see 58Bxx] 57R56 %Topological quantum field theories } \Keywords{ Planar Algebras, Quantum Groups, Fusion Categories, Knot Theory, Link Invariants }