Frobenius algebras and 2D topological quantum field theories

By: Kock JoachimMaterial type: TextTextSeries: London Mathematical Society Student Texts ; 59Publication details: Cambridge, U.K.: Cambridge University Press, [c2004]Description: 240 pISBN: 9780521540315Subject(s): MathematicsLOC classification: QA251.5
Contents:
1 - Cobordisms and topological quantum field theories 2 - Frobenius algebras 3 - Monoids and monoidal categories
Summary: 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. --- summary provided by publisher
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Item type Current library Collection Shelving location Call number Status Notes Date due Barcode Item holds
Book Book ICTS
Mathematic Rack No 5 QA251.5 (Browse shelf (Opens below)) Available Invoice no. IN00 7092 ; Date 22-02-2019 01729
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1 - Cobordisms and topological quantum field theories
2 - Frobenius algebras
3 - Monoids and monoidal categories

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. --- summary provided by publisher

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