Geodesic
Arithmetic Invariants of Simplicial Complexes
Canadian journal of mathematics, Tome 32 (1980) no. 6, pp. 1306-1310

Voir la notice de l'article provenant de la source Cambridge University Press

What invariants of a finite simplicial complex K can be computed solely from the values v0(K), V1(K), ..., v i(K), ... where V i(K) is the number of i-simplexes of K? The Euler chracteristic χ(K) = Σ i (– 1)i v i (K) is a subdivision invariant and a homotopy invariant while the dimension of K is a subdivision invariant and homeomorphism invariant. In [3], Wall has shown that the Euler chracteristic is the only linear function to the integers that is a subdivision invariant. In this paper we show that the only subdivision invariants (linear or not) of K are the Euler characteristic and the dimension. More precisely we prove the following theorem. 
Brown, M.; Wasserman, A. G. Arithmetic Invariants of Simplicial Complexes. Canadian journal of mathematics, Tome 32 (1980) no. 6, pp. 1306-1310. doi: 10.4153/CJM-1980-100-0
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[1] 1. Glaser, L., Geometrical combinatorial topology (Van Nostrand, 1970). Google Scholar

[2] 2. Rushing, T. B., Topological embeddings (Academic Press, N.Y., 1973). Google Scholar

[3] 3. Wall, C. T. C., Arithmetic properties of simplicial complexes, Can. J. Math. 18 (1966), 92–96. Google Scholar

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