Diagrammatic Algebra

ISBN-13: 9781470466718

J. Scott Carter;Seiichi Kamada

Opis

This book is an introduction to techniques and results in diagrammatic algebra. It starts with abstract tensors and their categorifications, presents diagrammatic methods for studying Frobenius and Hopf algebras, and discusses their relations with topological quantum field theory and knot theory. The text is replete with figures, diagrams, and suggestive typography that allows the reader a glimpse into many higher dimensional processes. The penultimate chapter summarizes the previous material by demonstrating how to braid 3- and 4- dimensional manifolds into 5- and 6-dimensional spaces. The book is accessible to post-qualifier graduate students, and will also be of interest to algebraists, topologists and algebraic topologists who would like to incorporate diagrammatic techniques into their research.

Spis treści

• Introduction
• Elements
• Planar trivalent diagrams
• The multi-category FA
• Triple arrows for FA
• Surfaces in 3-space
• Beyond surfaces
• Parentheses and so forth
• Knots in space
• Foams and surfaces in 4-space
• Higher dimensional braids
• Globular multi-categories
• Bibliography
• Index