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Mat. Zametki, 1968, Volume 3, Issue 5, Pages 511–522 (Mi mz6708)  

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 $i\ge0$.

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English version:
Mathematical Notes, 1968, 3:5, 326–332

Bibliographic databases:

UDC: 513.83
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

Citation in format AMSBIB
\Bibitem{Gro68}
\by M.~L.~Gromov
\paper On the number of simplexes of subdivisions of finite complexes
\jour Mat. Zametki
\yr 1968
\vol 3
\issue 5
\pages 511--522
\mathnet{http://mi.mathnet.ru/mz6708}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=227971}
\zmath{https://zbmath.org/?q=an:0169.55401|0157.53804}
\transl
\jour Math. Notes
\yr 1968
\vol 3
\issue 5
\pages 326--332
\crossref{https://doi.org/10.1007/BF01150983}


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