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 Mat. Zametki: Year: Volume: Issue: Page: Find

 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 $i\ge0$.

Full text: PDF file (909 kB)

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

Bibliographic databases:

UDC: 513.83

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}