Quasi-quantum groups, knots, three-manifolds, and topological field theory

We show how to construct, starting from a quasi-Hopf algebra, or quasi-quantum group, invariants of knots and links. In some cases, these invariants give rise to invariants of the three-manifolds obtained by surgery along these links. This happens for a finite-dimensional quasi-quantum group, whose...

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Detalles Bibliográficos
Autores principales: Altschüler, D R, Costé, A
Lenguaje:eng
Publicado: 1992
Materias:
Particle Physics - Theory
Acceso en línea:https://dx.doi.org/10.1007/BF02096567
http://cds.cern.ch/record/230999
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author Altschüler, D R
Costé, A
author_facet Altschüler, D R
Costé, A
author_sort Altschüler, D R
collection CERN
description We show how to construct, starting from a quasi-Hopf algebra, or quasi-quantum group, invariants of knots and links. In some cases, these invariants give rise to invariants of the three-manifolds obtained by surgery along these links. This happens for a finite-dimensional quasi-quantum group, whose definition involves a finite group $G$, and a 3-cocycle $\om$, which was first studied by Dijkgraaf, Pasquier and Roche. We treat this example in more detail, and argue that in this case the invariants agree with the partition function of the topological field theory of Dijkgraaf and Witten depending on the same data $G, \,\om$.
id cern-230999
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 1992
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spelling cern-2309992019-09-30T06:29:59Zdoi:10.1007/BF02096567http://cds.cern.ch/record/230999engAltschüler, D RCosté, AQuasi-quantum groups, knots, three-manifolds, and topological field theoryParticle Physics - TheoryWe show how to construct, starting from a quasi-Hopf algebra, or quasi-quantum group, invariants of knots and links. In some cases, these invariants give rise to invariants of the three-manifolds obtained by surgery along these links. This happens for a finite-dimensional quasi-quantum group, whose definition involves a finite group $G$, and a 3-cocycle $\om$, which was first studied by Dijkgraaf, Pasquier and Roche. We treat this example in more detail, and argue that in this case the invariants agree with the partition function of the topological field theory of Dijkgraaf and Witten depending on the same data $G, \,\om$.hep-th/9202047CERN-TH-6360-92CPT-2634LAPP-TH-342oai:cds.cern.ch:2309991992
spellingShingle Particle Physics - Theory
Altschüler, D R
Costé, A
Quasi-quantum groups, knots, three-manifolds, and topological field theory
title Quasi-quantum groups, knots, three-manifolds, and topological field theory
title_full Quasi-quantum groups, knots, three-manifolds, and topological field theory
title_fullStr Quasi-quantum groups, knots, three-manifolds, and topological field theory
title_full_unstemmed Quasi-quantum groups, knots, three-manifolds, and topological field theory
title_short Quasi-quantum groups, knots, three-manifolds, and topological field theory
title_sort quasi-quantum groups, knots, three-manifolds, and topological field theory
topic Particle Physics - Theory
url https://dx.doi.org/10.1007/BF02096567
http://cds.cern.ch/record/230999
work_keys_str_mv AT altschulerdr quasiquantumgroupsknotsthreemanifoldsandtopologicalfieldtheory
AT costea quasiquantumgroupsknotsthreemanifoldsandtopologicalfieldtheory

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