On the number of simplexes of subdivisions of finite complexes

M. L. Gromov

doi:10.1007/BF01150983

On the number of simplexes of subdivisions of finite complexes

M. L. Gromov

Mathematics

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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)
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	https://doi.org/10.1007/BF01150983
State	Published - May 1968

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General Mathematics

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title = "On the number of simplexes of subdivisions of finite complexes",

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.",

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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.

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On the number of simplexes of subdivisions of finite complexes

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