This 2003 book describes a striking connection between topology and algebra, namely that 2D topological quantum field theories are equivalent to commutative Frobenius algebras. The precise formulation of the theorem and its proof is given in terms of monoidal categories, and the main purpose of the book is to develop these concepts from an elementary level, and more generally serve as an introduction to categorical viewpoints in mathematics. Rather than just proving the theorem, it is shown how the result fits into a more general pattern concerning universal monoidal categories for algebraic structures. Throughout, the emphasis is on the interplay between algebra and topology, with graphical interpretation of algebraic operations, and topological structures described algebraically in terms of generators and relations. The book will prove valuable to students or researchers entering this field who will learn a host of modern techniques that will prove useful for future work.Read more
- Teaches reader a range of modern techniques that will be valuable in future work
- Framed in modern language of category theory
- Includes numerous exercises and examples to help use for study
Reviews & endorsements
'This book is a solid introduction to some important ideas of contemporary interest. It is very pleasant to read, and its ample collection of exercises includes interesting examples in addition to tests of basic understanding.' Mathematical Reviews
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- Date Published: December 2003
- format: Paperback
- isbn: 9780521540315
- length: 258 pages
- dimensions: 229 x 152 x 15 mm
- weight: 0.38kg
- contains: 60 b/w illus.
- availability: Available
Table of Contents
1. Cobordisms and TQFTs
2. Frobenius algebras
3. Monoids and monoidal categories
Appendix. Vocabulary from category theory.
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