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Monoidal Categories and Topological Field Theory (Hardcover, 1st ed. 2017)
Loot Price: R5,687
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Monoidal Categories and Topological Field Theory (Hardcover, 1st ed. 2017)
Series: Progress in Mathematics, 322
Expected to ship within 12 - 17 working days
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This monograph is devoted to monoidal categories and their
connections with 3-dimensional topological field theories. Starting
with basic definitions, it proceeds to the forefront of current
research. Part 1 introduces monoidal categories and several of
their classes, including rigid, pivotal, spherical, fusion,
braided, and modular categories. It then presents deep theorems of
Muger on the center of a pivotal fusion category. These theorems
are proved in Part 2 using the theory of Hopf monads. In Part 3 the
authors define the notion of a topological quantum field theory
(TQFT) and construct a Turaev-Viro-type 3-dimensional state sum
TQFT from a spherical fusion category. Lastly, in Part 4 this
construction is extended to 3-manifolds with colored ribbon graphs,
yielding a so-called graph TQFT (and, consequently, a 3-2-1
extended TQFT). The authors then prove the main result of the
monograph: the state sum graph TQFT derived from any spherical
fusion category is isomorphic to the Reshetikhin-Turaev surgery
graph TQFT derived from the center of that category. The book is of
interest to researchers and students studying topological field
theory, monoidal categories, Hopf algebras and Hopf monads.
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