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Matematicheskie Zametki, 1968, Volume 3, Issue 5, Pages 511–522
(Mi mzm6708)
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This article is cited in 3 scientific papers (total in 3 papers)
On the number of simplexes of subdivisions of finite complexes
M. L. Gromov Leningrad State University named after A. A. Zhdanov
Abstract:
Combinatorial invariants of a finite simplicial complex $K$ are considered that are functions of the number $\alpha_i(K)$ of Simplexes of dimension $i$ of this complex. The main result is Theorem 2, which gives the necessary and sufficient condition for two complexes $K$ and $L$ to have subdivisions $K'$ and $L'$ such that $\alpha_i(K')=\alpha_i(L')$ for $0\le i<\infty$. The theorem yields a corollary: if the polyhedra $|K|$ and $|L|$ are homeomorphic, then there exist subdivisions $K'$ and $L'$ such that $\alpha_i(K')=\alpha_i(L')$ for $i\ge0$.
Received: 11.09.1967
Citation:
M. L. Gromov, “On the number of simplexes of subdivisions of finite complexes”, Mat. Zametki, 3:5 (1968), 511–522; Math. Notes, 3:5 (1968), 326–332
Linking options:
https://www.mathnet.ru/eng/mzm6708 https://www.mathnet.ru/eng/mzm/v3/i5/p511
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Abstract page: | 278 | Full-text PDF : | 146 | First page: | 1 |
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