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We define an invariant $\nabla_G(M)$ of pairs M,G, where M is a 3-manifold obtained by surgery on some framed link in the cylinder $S\times I$, S is a connected surface with at least one boundary component, and G is a fatgraph spine of S.
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N. Kawazumi, private communication
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D. Cheptea, T.T.Q. Le, A TQFT associated to the LMO invariant of three-dimensional manifolds , Comm. Math. Phys. 272
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S. Morita, R.C. Penner, Torelli groups, extended Johnson homomorphisms, and new cycles on the moduli space of curves , Math. Proc. Camb. Philos. Soc. 144
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2009
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