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Diagrammatic Algebra
 
J. Scott Carter University of South Alabama, Mobile, AL
Seiichi Kamada Osaka University, Osaka, Japan
Diagrammatic Algebra
Softcover ISBN:  978-1-4704-6671-8
Product Code:  SURV/264
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
eBook ISBN:  978-1-4704-6815-6
Product Code:  SURV/264.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-6671-8
eBook: ISBN:  978-1-4704-6815-6
Product Code:  SURV/264.B
List Price: $250.00 $187.50
MAA Member Price: $225.00 $168.75
AMS Member Price: $200.00 $150.00
Diagrammatic Algebra
Click above image for expanded view
Diagrammatic Algebra
J. Scott Carter University of South Alabama, Mobile, AL
Seiichi Kamada Osaka University, Osaka, Japan
Softcover ISBN:  978-1-4704-6671-8
Product Code:  SURV/264
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
eBook ISBN:  978-1-4704-6815-6
Product Code:  SURV/264.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-6671-8
eBook ISBN:  978-1-4704-6815-6
Product Code:  SURV/264.B
List Price: $250.00 $187.50
MAA Member Price: $225.00 $168.75
AMS Member Price: $200.00 $150.00
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 2642021; 365 pp
    MSC: Primary 18; 55; 57

    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.

    Readership

    Graduate students and researchers interested in homological algebra, category theory, and diagrammatic calculus.

  • Table of Contents
     
     
    • Chapters
    • 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
  • Additional Material
     
     
  • Reviews
     
     
    • With an engaging expository style along with effective use of visualization and typography that in many ways embodies the philosophical principles behind diagrammatic reasoning itself, this book offers an insightful exploration of some state-of-the-art perspectives on algebra from a diagrammatic viewpoint.

      Timothy Clark, Loyola University Maryland
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2642021; 365 pp
MSC: Primary 18; 55; 57

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.

Readership

Graduate students and researchers interested in homological algebra, category theory, and diagrammatic calculus.

  • Chapters
  • 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
  • With an engaging expository style along with effective use of visualization and typography that in many ways embodies the philosophical principles behind diagrammatic reasoning itself, this book offers an insightful exploration of some state-of-the-art perspectives on algebra from a diagrammatic viewpoint.

    Timothy Clark, Loyola University Maryland
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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