On the number of simplexes of subdivisions of finite complexes

Mikhael Gromov

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)326-332
Number of pages7
JournalMathematical Notes of the Academy of Sciences of the USSR
Volume3
Issue number5
DOIs
StatePublished - May 1968

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Subdivision
Simplicial Complex
Homeomorphic
Theorem
Polyhedron
Corollary
Necessary Conditions
Invariant
Sufficient Conditions

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

In: Mathematical Notes of the Academy of Sciences of the USSR, Vol. 3, No. 5, 05.1968, p. 326-332.

Research output: Contribution to journalArticle

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