Geodesic
Pachner Move $3\to 3$ and Affine Volume-Preserving Geometry in $\mathbb R^3$
Symmetry, integrability and geometry: methods and applications, Tome 1 (2005) Cet article a éte moissonné depuis la source Math-Net.Ru

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Pachner move $3\to 3$ deals with triangulations of four-dimensional manifolds. We present an algebraic relation corresponding in a natural way to this move and based, a bit paradoxically, on three-dimensional geometry.
Keywords: piecewise-linear topology; Pachner move; algebraic relation; three-dimensional affine geometry. 
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     title = {Pachner {Move} $3\to 3$ and {Affine} {Volume-Preserving} {Geometry} in~$\mathbb R^3$},
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Igor G. Korepanov. Pachner Move $3\to 3$ and Affine Volume-Preserving Geometry in $\mathbb R^3$. Symmetry, integrability and geometry: methods and applications, Tome 1 (2005). http://geodesic.mathdoc.fr/item/SIGMA_2005_1_a20/

[1] Lickorish W. B. R., “Simplicial moves on complexes and manifolds”, Proceedings of the Kirbyfest, Geom. Topol. Monographs, 2, 1999, 299–320 ; arXiv:math.GT/9911256 | MR | Zbl

[2] Diatta A., Medina A., “Classical Yang–Baxter equation and left invariant affine geometry on Lie groups”, Manuscripta Mathematica, 114:4 (2004), 477–486 ; arXiv:math.DG/0203198 | DOI | MR | Zbl

[3] Korepanov I. G., A formula with volumes of five tetrahedra and discrete curvature, arXiv:nlin.SI/0003001

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

[5] Korepanov I. G., “Invariants of PL manifolds from metrized simplicial complexes. Three-dimensional case”, J. Nonlinear Math. Phys., 8:2 (2001), 196–210 ; arXiv:math.GT/0009225 | DOI | MR | Zbl

[6] Korepanov I. G., Martyushev E. V., “A classical solution of the pentagon equation related to the group $SL(2)$”, Theor. Math. Phys., 129:1 (2001), 1320–1324 | DOI | MR | Zbl

[7] Ponzano G., Regge T., “Semi-classical limit of Racah coefficients”, Spectroscopic and Group Theoretical Methods in Physics, ed. F. Bloch, North-Holland, 1968, 1–58

[8] Roberts J., “Classical $6j$-symbols and the tetrahedron”, Geom. Topol., 3 (1999), 21–66 ; arXiv:math-ph/9812013 | DOI | MR | Zbl

[9] Taylor Y., Woodward C., Spherical tetrahedra and invariants of 3-manifolds, arXiv:math.GT/0406228

[10] Korepanov I. G., “$SL(2)$-Solution of the pentagon equation and invariants of three-dimensional manifolds”, Theor. Math. Phys., 138:1 (2004), 18–27 ; arXiv:math.AT/0304149 | DOI | MR | Zbl

[11] Korepanov I. G., “Euclidean 4-simplices and invariants of four-dimensional manifolds: I. Moves $3\to3$”, Theor. Math. Phys., 131:3 (2002), 765–774 ; arXiv:math.GT/0211165 | DOI | MR | Zbl

[12] Korepanov I. G., “Euclidean 4-simplices and invariants of four-dimensional manifolds: II. An algebraic complex and moves $2\leftrightarrow 4$”, Theor. Math. Phys., 133:1 (2002), 1338–1347 ; arXiv:math.GT/0211166 | DOI | MR | Zbl

[13] Korepanov I. G., “Euclidean 4-simplices and invariants of four-dimensional manifolds: III. Moves $1\leftrightarrow 5$ and related structures”, Theor. Math. Phys., 135:2 (2003), 601–613 ; arXiv:math.GT/0211167 | DOI | MR | Zbl

[14] Atiyah M. F., “Topological quantum field theory”, Publications Mathématiques de l'IHÉS, 68 (1988), 175–186 | MR | Zbl