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Frobenius Algebras and 2-D Topological Quantum Field Theories Joachim Kock (Universite de Nice, Sophia Antipolis)

Frobenius Algebras and 2-D Topological Quantum Field Theories By Joachim Kock (Universite de Nice, Sophia Antipolis)

Frobenius Algebras and 2-D Topological Quantum Field Theories by Joachim Kock (Universite de Nice, Sophia Antipolis)


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Summary

This 2003 book proves striking results connecting topology and algebra and shows how the result fits into a more general pattern. It will prove valuable to students or researchers entering this field who will learn a host of modern techniques. There are numerous exercises and examples making the book suitable for teaching.

Frobenius Algebras and 2-D Topological Quantum Field Theories Summary

Frobenius Algebras and 2-D Topological Quantum Field Theories by Joachim Kock (Universite de Nice, Sophia Antipolis)

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.

Frobenius Algebras and 2-D Topological Quantum Field Theories Reviews

'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

Table of Contents

1. Cobordisms and TQFTs; 2. Frobenius algebras; 3. Monoids and monoidal categories; Appendix. Vocabulary from category theory.

Additional information

NLS9780521540315
9780521540315
0521540313
Frobenius Algebras and 2-D Topological Quantum Field Theories by Joachim Kock (Universite de Nice, Sophia Antipolis)
New
Paperback
Cambridge University Press
2003-12-04
258
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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