A TQFT associated to the LMO invariant of three-dimensional manifolds

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dc.creatorCheptea, Dorin
dc.creatorLe, Thang T Q
dc.date2005-08-12
dc.date2006-02-06
dc.date.accessioned2026-07-07T10:30:24Z
dc.date.available2026-07-07T10:30:24Z
dc.descriptionWe construct a Topological Quantum Field Theory (in the sense of Atiyah) associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from the category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category. It is built together with its truncations with respect to a natural grading, and we prove that these TQFTs are non-degenerate and anomaly-free. The TQFT(s) induce(s) a (series of) representation(s) of a subgroup ${\cal L}_g$ of the Mapping Class Group that contains the Torelli group. The N=1 truncation produces a TQFT for the Casson-Walker-Lescop invariant.
dc.description28 pages, 13 postscript figures. Version 2 (Section 1 has been considerably shorten, and section 3 has been slightly shorten, since they will constitute a separate paper. Section 4, which contained only announce of results, has been suprimated; it will appear in detail elsewhere. Consequently some statements have been re-numbered. No mathematical changes have been made.)
dc.identifierhttps://arxiv.org/abs/math/0508220
dc.identifierhttp://arxiv.org/abs/math/0508220
dc.identifierCommun.Math.Phys.272:601-634,2007
dc.identifierdoi:10.1007/s00220-007-0241-3
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/178122
dc.subjectGeometric Topology
dc.subjectQuantum Algebra
dc.subject57M27 (primarily), 57R56, 81T45, 81Q30, 81R50
dc.titleA TQFT associated to the LMO invariant of three-dimensional manifolds
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