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

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

2005-08-12

arxiv.org/abs/math/0508220v2

Commun.Math.Phys.272:601-634,2007

Mathematics

Geometric Topology

28 pages, 13 postscript figures. Version 2 (Section 1 has been considerably shorten, and section 3 has been slightly shorten,

Scientific paper

10.1007/s00220-007-0241-3

We 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.

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