WorldCat Identities

Virelizier, Alexis

Overview
Works: 6 works in 12 publications in 2 languages and 53 library holdings
Roles: Author
Classifications: QA612.7, 514.24
Publication Timeline
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Most widely held works by Alexis Virelizier
Homotopy quantum field theory by V. G Turaev( Book )

4 editions published in 2010 in English and held by 39 WorldCat member libraries worldwide

Homotopy Quantum Field Theory (HQFT) is a branch of Topological Quantum Field Theory founded by E. Witten and M. Atiyah. It applies ideas from theoretical physics to study principal bundles over manifolds and, more generally, homotopy classes of maps from manifolds to a fixed target space. This book is the first systematic exposition of Homotopy Quantum Field Theory. It starts with a formal definition of an HQFT and provides examples of HQFTs in all dimensions. The main body of the text is focused on 2-dimensional and 3-dimensional HQFTs. A study of these HQFTs leads to new algebraic objects: crossed Frobenius group-algebras, crossed ribbon group-categories, and Hopf group-coalgebras. These notions and their connections with HQFTs are discussed in detail. The text ends with several appendices including an outline of recent developments and a list of open problems. Three appendices by M. Müger and A. Virelizier summarize their work in this area. The book is addressed to mathematicians, theoretical physicists, and graduate students interested in topological aspects of quantum field theory. The exposition is self-contained and well suited for a one-semester graduate course. Prerequisites include only basics of algebra and topology
Algèbres de Hopf graduées et fibrés plats sur les 3-variétés by Alexis Virelizier( Book )

4 editions published in 2001 in French and English and held by 10 WorldCat member libraries worldwide

Involutory Hopf group-coalgebras and flat bundles over 3-manifolds by Alexis Virelizier( )

1 edition published in 2005 in English and held by 1 WorldCat member library worldwide

Materiały z II International Conference "Knots in Poland 2003", Warszawa, Będlewo
Hopf diagrams and quantum invariants( )

1 edition published in 2005 in English and held by 1 WorldCat member library worldwide

Hopf diagrams and quantum invariants by Alain Bruguières( Book )

1 edition published in 2005 in English and held by 1 WorldCat member library worldwide

Surgery HQFT by V. G Turaev( )

1 edition published in 2013 in English and held by 1 WorldCat member library worldwide

Homotopy Quantum Field Theories (HQFTs) generalize more familiar Topological Quantum Field Theories (TQFTs). In generalization of the surgery construction of 3-dimensional TQFTs from modular categories, we use surgery to derive 3-dimensional HQFTs from G-modular categories
 
Audience Level
0
Audience Level
1
  Kids General Special  
Audience level: 0.79 (from 0.74 for Homotopy q ... to 0.99 for Involutory ...)

Homotopy quantum field theory
Alternative Names
Virelizier, Alexis

Languages
English (10)

French (2)

Covers