Geodesic
Euclidean 4-Simplices and Invariants of Four-Dimensional Manifolds: I. Moves $3\to 3$.
Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 3, pp. 377-388

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We construct invariants of four-dimensional piecewise linear manifolds, represented as simplicial complexes, with respect to moves that transform a cluster of three 4-simplices having a common two-dimensional face to a different cluster of the same type and having the same boundary. Our construction is based on using Euclidean geometric quantities. 
@article{TMF_2002_131_3_a1,
     author = {I. G. Korepanov},
     title = {Euclidean {4-Simplices} and {Invariants} of {Four-Dimensional} {Manifolds:} {I.} {Moves} $3\to 3$.},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {377--388},
     publisher = {mathdoc},
     volume = {131},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_131_3_a1/}
}
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I. G. Korepanov. Euclidean 4-Simplices and Invariants of Four-Dimensional Manifolds: I. Moves $3\to 3$.. Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 3, pp. 377-388. http://geodesic.mathdoc.fr/item/TMF_2002_131_3_a1/