Frobenius Algebras and 2-D Topological Quantum Field Theories

This 2003 book connects topology and algebra using modern techniques. Numerous exercises and examples, ideal for course use.

Joachim Kock (Author)

9780521540315, Cambridge University Press

Paperback, published 4 December 2003

258 pages, 60 b/w illus.
22.9 x 15.2 x 1.5 cm, 0.37 kg

'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

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.

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

Subject Areas: Applied mathematics [PBW], Topology [PBP], Geometry [PBM]