Observables in the Turaev-Viro and Crane-Yetter models

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dc.creatorBarrett, John W.
dc.creatorGarcia-Islas, J. Manuel
dc.creatorMartins, Joao Faria
dc.date2004-11-12
dc.date2007-01-09
dc.date.accessioned2026-07-07T11:32:27Z
dc.date.available2026-07-07T11:32:27Z
dc.descriptionWe define an invariant of graphs embedded in a three-manifold and a partition function for 2-complexes embedded in a triangulated four-manifold by specifying the values of variables in the Turaev-Viro and Crane-Yetter state sum models. In the case of the three-dimensional invariant, we prove a duality formula relating its Fourier transform to another invariant defined via the coloured Jones polynomial. In the case of the four-dimensional partition function, we give a formula for it in terms of a regular neighbourhood of the 2-complex and the signature of its complement. Some examples are computed which show that the partition function determines an invariant which can detect non locally-flat surfaces in a four-manifold.
dc.descriptionApprox 26 pages. v2: 4d results substantially extended
dc.identifierhttps://arxiv.org/abs/math/0411281
dc.identifierhttp://arxiv.org/abs/math/0411281
dc.identifierJ.Math.Phys.48:093508,2007
dc.identifierdoi:10.1063/1.2759440
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/197601
dc.subjectQuantum Algebra
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectMathematical Physics
dc.subjectGeometric Topology
dc.titleObservables in the Turaev-Viro and Crane-Yetter models
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