Frobenius Algebras and 2-D Topological Quantum Field Theories (London Mathematical Society Student Texts Book 59) by Joachim Kock (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I love this book very much. And I do think this is beneficial to undergraduates who have taken some abstract algebra and topology. The algebraic maturity required is way more than the topology. For me the idea of generalizing algebraic object to any monoidal categories was only introduced to me after I’ve had years of exposure to algebra having taking several courses in representation theory and commutative/ noncommutative algebra. That said, the writing is so good and I think people with modest background can still understand most of the chapters. I personally finished reading the whole book in two days. It’s just so good!

⭐This is a very well-written book. It claims to be for undergrads, and although the category theory is nicely handled, you’d need some serious abstraction to keep going.

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