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## Some cellular subdivisions of simplicial complexes

Mardešić, Sibe
Some cellular subdivisions of simplicial complexes // Glasnik matematički, 45 (2010), 1; 219-290 (međunarodna recenzija, članak, znanstveni)

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Naslov
Some cellular subdivisions of simplicial complexes

Autori
Mardešić, Sibe

Izvornik
Glasnik matematički (0017-095X) 45 (2010), 1; 219-290

Ključne riječi
convex polytope; simplicial complex; cellular complex; subdivision of a complex; isomorphism of cellular complexes; resolution of a space; shape.

Sažetak
In a previous paper the author has associated with every inverse system of compact CW-complexes _X_ with limit X and every simplicial complex K with geometric realization |K| a resolution of X x |K|, which consists of spaces having the homotopy type of polyhedra. In a subsequent paper it was shown that this construction is functorial. The proof depends essentially on particular cellular subdivisions of K. The purpose of this paper is to describe in detail these subdivisions and establish their relevant properties. In particular, one defines two subdivisions L(K) and N(K) of K. Each cell from L(K), respectively from N(K), is contained in a simplex \sigma in K and it is the direct sum a + b, respectively c + d, of certain simplices contained in \sigma. One defines new subdivisions L'(K) and N'(K) of K by taking for their cells the direct sums L(a) + b, respectively c + N(d). The main result asserts that there is an isomorphism of cellular complexes \theta: L'(K) --> N'(K), which induces a selfhomeomorphism \Theta: |K| --> |K|.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Projekt / tema
037-0372791-2802 - Teorija dimenzije i oblika (Sibe Mardešić, )

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb

Profili: Sibe Mardešić (autor)

#### Citiraj ovu publikaciju

Mardešić, Sibe
Some cellular subdivisions of simplicial complexes // Glasnik matematički, 45 (2010), 1; 219-290 (međunarodna recenzija, članak, znanstveni)
Mardešić, S. (2010) Some cellular subdivisions of simplicial complexes. Glasnik matematički, 45 (1), 219-290.
@article{article, author = {Marde\v{s}i\'{c}, S.}, year = {2010}, pages = {219-290}, keywords = {convex polytope, simplicial complex, cellular complex, subdivision of a complex, isomorphism of cellular complexes, resolution of a space, shape.}, journal = {Glasnik matemati\v{c}ki}, volume = {45}, number = {1}, issn = {0017-095X}, title = {Some cellular subdivisions of simplicial complexes}, keyword = {convex polytope, simplicial complex, cellular complex, subdivision of a complex, isomorphism of cellular complexes, resolution of a space, shape.} }

#### Časopis indeksira:

• Web of Science Core Collection (WoSCC)
• Science Citation Index Expanded (SCI-EXP)
• SCI-EXP, SSCI i/ili A&HCI
• Scopus

#### Uključenost u ostale bibliografske baze podataka:

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