Euclidean 4-simplices and invariants of four-dimensional manifolds: I.   Moves 3 -> 3
  We construct invariants of four-dimensional piecewise-linear manifolds, represented as simplicial complexes, with respect to rebuildings that transform a cluster of three 4-simplices having a common two-dimensional face in a different cluster of the same type and having the same boundary. Our construction is based on the usage of Euclidean geometric values. 
Igor G. Korepanov