| 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 |
| 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 |
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Book DetailsMathematical Surveys and MonographsVolume: 264; 2021; 365 ppMSC: 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.
ReadershipGraduate students and researchers interested in homological algebra, category theory, and diagrammatic calculus.
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Table of Contents
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Chapters
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Introduction
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Elements
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Planar trivalent diagrams
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The multi-category FA
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Triple arrows for FA
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Surfaces in 3-space
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Beyond surfaces
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Parentheses and so forth
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Knots in space
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Foams and surfaces in 4-space
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Higher dimensional braids
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Globular multi-categories
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Additional Material
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Reviews
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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
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
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- Additional Material
- Reviews
- Requests
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.
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
