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101 0 $aeng
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181   $ctxt$2rdacontent
182   $cc$2rdamedia
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200 10$aHomotopy Quantum Field Theory $eWith Appendices by Michael Müger and Alexis Virelizier /$fVladimir Turaev
210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2010
215   $a1 online resource (290 pages)
225 0 $aEMS Tracts in Mathematics (ETM)$v10
330   $aHomotopy 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. Mu?ger 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.
606   $aAlgebraic topology$2bicssc
606   $aManifolds and cell complexes$2msc
606   $aAssociative rings and algebras$2msc
606   $aCategory theory; homological algebra$2msc
606   $aQuantum theory$2msc
615 07$aAlgebraic topology
615 07$aManifolds and cell complexes
615 07$aAssociative rings and algebras
615 07$aCategory theory; homological algebra
615 07$aQuantum theory
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700   $aTuraev$b Vladimir$067205
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906   $aBOOK
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996   $aHomotopy Quantum Field Theory$92564455
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