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 
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/
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     title = {Euclidean {4-Simplices} and {Invariants} of {Four-Dimensional} {Manifolds:} {I.} {Moves} $3\to 3$.},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] I. G. Korepanov, J. Nonlinear Math. Phys., 8:2 (2001), 196–210 | DOI | MR | Zbl

[2] I. G. Korepanov, E. V. Martyushev, J. Nonlinear Math. Phys., 9:1 (2002), 86–98 | DOI | MR | Zbl

[3] I. G. Korepanov, A formula with hypervolumes of six 4-simplices and two discrete curvatures, E-print nlin.SI/0003024

[4] J. Milnor, “The Schläfli differential equality”, Collected Papers. V. 1. Geometry, Publish or Perish, Houston, Texas, 1993, 281–295 | MR

[5] I. G. Korepanov, TMF, 124:1 (2000), 169–176 | DOI | MR | Zbl