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Diagrammatic Morphisms and Applications
Edited by: David E. Radford, University of Illinois at Chicago, IL, Fernando J. O. Souza, University of Iowa, Iowa City, IA, and David N. Yetter, Kansas State University, Manhattan, KS
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Contemporary Mathematics
2003; 213 pp; softcover
Volume: 318
ISBN-10: 0-8218-2794-4
ISBN-13: 978-0-8218-2794-9
List Price: US$65
Member Price: US$52
Order Code: CONM/318
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The technique of diagrammatic morphisms is an important ingredient in comprehending and visualizing certain types of categories with structure. It was widely used in this capacity in many areas of algebra, low-dimensional topology and physics. It was also applied to problems in classical and quantum information processing and logic.

This volume contains articles based on talks at the Special Session, "Diagrammatic Morphisms in Algebra, Category Theory, and Topology", at the AMS Sectional Meeting in San Francisco. The articles describe recent achievements in several aspects of diagrammatic morphisms and their applications. Some of them contain detailed expositions on various diagrammatic techniques. The introductory article by D. Yetter is a thorough account of the subject in a historical perspective.

Readership

Research mathematicians interested in algebra, category theory, and low-dimensional topology.

Table of Contents

  • D. N. Yetter -- Diagrammatic morphisms
  • J. C. Baez -- Spin foam perturbation theory
  • J. W. Barrett -- Unlinked embedded graphs
  • Y. Bespalov and B. Drabant -- Report on cross product bialgebras in braided categories
  • J. S. Carter, S. Kamada, and M. Saito -- Diagrammatic computations for quandles and cocycle knot invariants
  • B. Day and R. Street -- Lax monoids, pseudo-operads, and convolution
  • M. Đ urđ evich -- Diagrammatic formulation of multi-braided quantum groups
  • C. Frohman and J. Kania-Bartoszynska -- A matrix model for quantum \(SL_2\)
  • L. H. Kauffman and D. Radford -- Bi-oriented quantum algebras, and a generalized Alexander polynomial for virtual links
  • T. Kerler -- Towards an algebraic characterization of 3-dimensional cobordisms
  • Z. Oziewicz -- Operad of graphs, convolution and quasi Hopf algebra
  • J. H. Przytycki and A. S. Sikora -- \(SU_n\)-quantum invariants for periodic links
  • R. Street -- Weak omega-categories
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