Communications in Mathematical Physics

, Volume 272, Issue 3, pp 601–634 | Cite as

A TQFT Associated to the LMO Invariant of Three-Dimensional Manifolds

  • Dorin ChepteaEmail author
  • Thang T. Q. Le


We construct a Topological Quantum Field Theory associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from a category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category. This 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 \({{\mathcal{L}}}_g\) of the Mapping Class Group that contains the Torelli group. The N =  1 truncation is a TQFT for the Casson-Walker-Lescop invariant.


Boundary Component Mapping Class Group Chord Diagram Chain Graph Link Component 
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© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Center for the Topology and Quantization of Moduli Spaces, Department of Mathematical SciencesUniversity of AarhusAarhus CDenmark
  2. 2.Institute of Mathematics of the Romanian AcademyBucharestRomania
  3. 3.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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