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  3. Frobenius Algebras and 2-D Topological Quantum Field Theories
  • Cited by 110
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    • Publisher:
      Cambridge University Press
      Publication date:
      January 2010
      December 2003
      ISBN:
      9780511615443
      9780521832670
      9780521540315
      DOI:
      https://doi.org/10.1017/CBO9780511615443
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.55kg, 258 Pages
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.37kg, 258 Pages
      • Subjects:
      Mathematics (general), Mathematics, Mathematical Physics
      Series:
      London Mathematical Society Student Texts (59)
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    Subjects:
    Mathematics (general), Mathematics, Mathematical Physics
    Series:
    London Mathematical Society Student Texts (59)
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    Book 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.

    Reviews

    'This book is a solid introduction to some important ideas of contemporary interest. It is very pleasant to read, and its ample collection of exercises includes interesting examples in addition to tests of basic understanding.'

    Source: Mathematical Reviews

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