### Abstract

Combinatorial invariants of a finite simplicial complex K are considered that are functions of the number α_{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 α_{i}(K')=α_{i}(L') for 0 ≤ ∞. The theorem yields a corollary: if the polyhedra |K| and |L| are homeomorphic, then there exist subdivisions K' and L' such that α_{i}(K')=α_{i}(L') for i≥0.

Original language | English (US) |
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Pages (from-to) | 326-332 |

Number of pages | 7 |

Journal | Mathematical Notes of the Academy of Sciences of the USSR |

Volume | 3 |

Issue number | 5 |

DOIs | |

State | Published - May 1968 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**On the number of simplexes of subdivisions of finite complexes.** / Gromov, Mikhael.

Research output: Contribution to journal › Article

*Mathematical Notes of the Academy of Sciences of the USSR*, vol. 3, no. 5, pp. 326-332. https://doi.org/10.1007/BF01150983

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TY - JOUR

T1 - On the number of simplexes of subdivisions of finite complexes

AU - Gromov, Mikhael

PY - 1968/5

Y1 - 1968/5

N2 - Combinatorial invariants of a finite simplicial complex K are considered that are functions of the number αi(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 αi(K')=αi(L') for 0 ≤ ∞. The theorem yields a corollary: if the polyhedra |K| and |L| are homeomorphic, then there exist subdivisions K' and L' such that αi(K')=αi(L') for i≥0.

AB - Combinatorial invariants of a finite simplicial complex K are considered that are functions of the number αi(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 αi(K')=αi(L') for 0 ≤ ∞. The theorem yields a corollary: if the polyhedra |K| and |L| are homeomorphic, then there exist subdivisions K' and L' such that αi(K')=αi(L') for i≥0.

UR - http://www.scopus.com/inward/record.url?scp=34250512490&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250512490&partnerID=8YFLogxK

U2 - 10.1007/BF01150983

DO - 10.1007/BF01150983

M3 - Article

VL - 3

SP - 326

EP - 332

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 5

ER -