Diagrammatics, singularities, and their algebraic interpretationsv

Abstract

Summary: ``This series of lectures reviews the remarkablefeature of quantum topology: There are unexpected directrelations among algebraic structures and the combinatorics ofknots and manifolds. The 6 j symbols, Hopf algebras,triangulations of 3 manifolds, Temperley Lieb algebra, and braidgroups are reviewed in the first three lectures. In the secondlecture, we discuss parentheses structures and 2 categories ofsurfaces in 3 space in relation to the Temperley Lieb algebras.In the fourth lecture, we give diagrammatics of 4 dimensionaltriangulations and their relations to the associahedron, a higherassociativity condition. We prove that the 4 dimensional Pachnermoves can be decomposed in terms of singular moves and lowerdimensional relations. In our last lecture, we give acombinatorial description of knotted surfaces in 4 space andtheir isotopies.''\par {For the entire collection see MR99b:55001.}