Geodesic
Complexity of 3-Manifolds and Combed 3-Manifolds
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology, discrete geometry, and set theory, Tome 252 (2006), pp. 83-93

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A new complexity, called a block number, is defined for a combed 3-manifold, and a method for the combinatorial classification of combed 3-manifolds with a given block number is proposed. 
@article{TM_2006_252_a8,
     author = {I. Ishii},
     title = {Complexity of {3-Manifolds} and {Combed} {3-Manifolds}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {83--93},
     publisher = {mathdoc},
     volume = {252},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2006_252_a8/}
}
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I. Ishii. Complexity of 3-Manifolds and Combed 3-Manifolds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology, discrete geometry, and set theory, Tome 252 (2006), pp. 83-93. http://geodesic.mathdoc.fr/item/TM_2006_252_a8/