Frobenius algebras and 2D topological quantum field theories

Joachim Kock - Collection London Mathematical Society Student Texts

254 pages, parution le 15/12/2003

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Résumé

This 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.

Sommaire

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

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Joachim Kock
Collection	London Mathematical Society Student Texts
Parution	15/12/2003
Nb. de pages	254
Format	15,2 x 22,6
Couverture	Broché
Poids	364g
Intérieur	Noir et Blanc
EAN13	9780521540315
ISBN13	978-0-521-54031-5