Abstract
We present sequences of linear maps of vector spaces with fixed bases. Each term of a sequence is a linear space of differentials of metric values ascribed to the elements of a simplicial complex determining a triangulation of a manifold. If a sequence is an acyclic complex, then we can construct a manifold invariant using its torsion. We demonstrate this first for three-dimensional manifolds and then construct the part of this program for four-dimensional manifolds pertaining to moves 2↔4.
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REFERENCES
I. G. Korepanov, Theor. Math. Phys., 131, 765-774 (2002).
I. G. Korepanov, J. Nonlinear Math. Phys., 8, 196–210 (2001).
I. G. Korepanov and E. V. Martyushev, J. Nonlinear Math. Phys., 9, 86–98 (2002).
J. Milnor, Bull. Amer. Math. Soc., 72, 358–426 (1966).
I. G. Korepanov and E. V. Martyushev, Theor. Math. Phys., 129, 1320–1324 (2001).
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Korepanov, I.G. Euclidean 4-Simplices and Invariants of Four-Dimensional Manifolds: II. An Algebraic Complex and Moves 2↔4. Theoretical and Mathematical Physics 133, 1338–1347 (2002). https://doi.org/10.1023/A:1020689829261
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DOI: https://doi.org/10.1023/A:1020689829261