Frobenius Algebras and 2-D Topological Quantum Field Theories (London Mathematical Society Student Texts, Series Number 59)

Describing a striking connection between topology and algebra, rather than only proving the theorem, this study demonstrates how the result fits into a more general pattern. Throughout the text 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. Includes numerous exercises and examples. 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. "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 the new quantum areas of mathematics, who will learn a host of modern techniques that will prove useful for future work."--Page 4 de la couverture "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 the new quantum areas of mathematics, who will learn a host of modern techniques that will prove useful for future work."--Jacket Proves striking results connecting topology and algebra and shows how the result fits into a more general pattern. The book 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 In the first section we recall some basic notions of manifolds with boundary and orientations, and Morse functions.