Frobenius algebras and 2D topological quantum field theories:
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...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2004
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| Schriftenreihe: | London Mathematical Society student texts
59 |
| Links: | https://doi.org/10.1017/CBO9780511615443 |
| Zusammenfassung: | 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. |
| Umfang: | 1 Online-Ressource (xiv, 240 Seiten) |
| ISBN: | 9780511615443 |
Internformat
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| spelling | Kock, Joachim 1967- Frobenius algebras and 2D topological quantum field theories Joachim Kock Frobenius Algebras & 2-D Topological Quantum Field Theories Cambridge Cambridge University Press 2004 1 Online-Ressource (xiv, 240 Seiten) txt c cr London Mathematical Society student texts 59 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. Erscheint auch als Druck-Ausgabe 9780521540315 Erscheint auch als Druck-Ausgabe 9780521832670 |
| spellingShingle | Kock, Joachim 1967- Frobenius algebras and 2D topological quantum field theories |
| title | Frobenius algebras and 2D topological quantum field theories |
| title_alt | Frobenius Algebras & 2-D Topological Quantum Field Theories |
| title_auth | Frobenius algebras and 2D topological quantum field theories |
| title_exact_search | Frobenius algebras and 2D topological quantum field theories |
| title_full | Frobenius algebras and 2D topological quantum field theories Joachim Kock |
| title_fullStr | Frobenius algebras and 2D topological quantum field theories Joachim Kock |
| title_full_unstemmed | Frobenius algebras and 2D topological quantum field theories Joachim Kock |
| title_short | Frobenius algebras and 2D topological quantum field theories |
| title_sort | frobenius algebras and 2d topological quantum field theories |
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