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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.

Euclidean 4-Simplices and Invariants of Four-Dimensional Manifolds: I. Moves 3→3