## Diagrammatics, Singularities, and Their Algebraic Interpretations (1996)

Venue: | in ``10th Brazilian Topology Meeting, Sa~ o Carlos, July 22 26, 1996,'' Mathematica Contempora^ nea |

Citations: | 12 - 2 self |

### BibTeX

@INPROCEEDINGS{Carter96diagrammatics,singularities,,

author = {J. Scott Carter and Louis H. Kauffman and Masahico Saito},

title = {Diagrammatics, Singularities, and Their Algebraic Interpretations},

booktitle = {in ``10th Brazilian Topology Meeting, Sa~ o Carlos, July 22 26, 1996,'' Mathematica Contempora^ nea},

year = {1996}

}

### OpenURL

### Abstract

This series of lectures reviews the remarkable feature of quantum topology: There are unexpected direct relations among algebraic structures and the combinatorics of knots and manifolds. The 6j symbols, Hopf algebras, triangulations of 3-manifolds, Temperley-Lieb algebra, and braid groups are reviewed in the first three lectures. In the second lecture, we discuss parentheses structures and 2-categories of surfaces in 3-space in relation to the Temperley-Lieb algebras. In the fourth lecture, we give diagrammatics of 4 dimensional triangulations and their relations to the associahedron, a higher associativity condition. We prove that the 4-dimensional Pachner moves can be decomposed in terms of singular moves, and lower dimensional relations. In our last lecture, we give a combinatorial description of knotted surfaces in 4-space and their isotopies. MRCN: 57Q45 Key words: Reidemeister Moves, 2-categories, Movie Moves, Knotted Surfaces 1 1 Introduction In this series of tal...