TY  - BOOK
AU  - Kock,Joachim
TI  - Frobenius algebras and 2D topological quantum field theories
T2  - London Mathematical Society student texts
SN  - 9780511615443 (ebook)
AV  - QA251.5 .K63 2004
U1  - 512/.24 21
PY  - 2004///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Frobenius algebras
KW  - Topological fields
KW  - Quantum field theory
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015)
N2  - 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
UR  - https://doi.org/10.1017/CBO9780511615443
ER  -