Geodesic
Euclidean 4-Simplices and Invariants of Four-Dimensional Manifolds: II. An Algebraic Complex and Moves $2\leftrightarrow 4$
Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 1, pp. 24-35 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $2\leftrightarrow 4$.
Keywords: piecewise-linear manifolds, manifold invariants Pachner moves, differential identities for Euclidean simplices
Mots-clés : acyclic complexes. 
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     author = {I. G. Korepanov},
     title = {Euclidean {4-Simplices} and {Invariants} of {Four-Dimensional} {Manifolds:} {II.} {An} {Algebraic} {Complex} and {Moves} $2\leftrightarrow 4$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {24--35},
     year = {2002},
     volume = {133},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_133_1_a1/}
}
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I. G. Korepanov. Euclidean 4-Simplices and Invariants of Four-Dimensional Manifolds: II. An Algebraic Complex and Moves $2\leftrightarrow 4$. Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 1, pp. 24-35. http://geodesic.mathdoc.fr/item/TMF_2002_133_1_a1/

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