Frobenius Algebras and 2-D Topological Quantum Field Theories

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Cambridge University Press, 2004 - Mathematics - 240 pages
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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.
  

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Contents

IV
1
V
9
VI
10
VIII
12
IX
15
X
18
XII
22
XIII
28
XXXVIII
135
XXXIX
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XL
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XLI
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XLII
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XLIII
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XLIV
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XLV
150

XIV
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XV
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XVI
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XVII
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XVIII
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XIX
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XX
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XXII
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XXIII
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XXIV
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XXV
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XXVI
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XXVII
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XXIX
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XXX
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XXXI
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XXXII
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XXXIII
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XXXIV
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XXXV
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XXXVI
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XXXVII
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XLVI
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XLVII
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XLVIII
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XLIX
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L
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LI
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LII
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LIII
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LIV
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LV
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LVI
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LVII
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LVIII
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LIX
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LX
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LXI
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LXII
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LXIII
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LXIV
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LXV
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LXVI
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Page 234 - BAEZ and JAMES DOLAN. Higher-dimensional algebra and topological quantum field theory. J. Math. Phys. 36 (1995), 6073-6105 (q-alg/9503002).
Page 234 - On algebraic structures implicit in topological quantum field theories, J. Knot Theory Ramifications 8 (1999), 125-163.
Page 236 - From subfactors to categories and topology I. Frobenius algebras in and Morita equivalence of tensor categories. J. Pure Appl. Alg. 180 (2003), 81-157 (math.CT/01 11204).

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