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

Dorin Cheptea; Thang T Q Le

doi:10.1007/s00220-007-0241-3

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

Dorin Cheptea·Thang T Q Le

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Abstract

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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BibTeX RIS

Dorin Cheptea, Thang T Q Le. 2006-02-06. A TQFT associated to the LMO invariant of three-dimensional manifolds. https://doi.org/10.1007/s00220-007-0241-3

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