On the Alexandroff-Borsuk problem

Matija Cencelj (Author), Umed H. Karimov (Author), Dušan Repovš (Author)

Abstract

Obravnavamo klasični problem Aleksandrova in Borsuka v kategoriji netriangulabilnih mnogoterosti: ali za dano ▫$n$▫-dimenzionalno kompaktno netriangulabilno mnogoterost ▫$M^n$▫ in dani ▫$\varepsilon > 0$▫ obstaja ▫$\varepsilon$▫-preslikava ▫$M^n$▫ na ▫$n$▫-dimenzionalni končni polieder, ki inducira homotopsko ekvivalenco?

Keywords

ANR;končni polieder;homotopska ekvivalenca;▫$\varepsilon$▫-preslikava;celularna preslikava;skoraj gladka mnogoterost;$|E_8|$-mnogoterost;Kirby-Siebenmannov razred;Galewski-Sternova ovira;netriangulabilna mnogoterost;problem Aleksandrova in Borsuka o mnogoterostih;finite polyhedron;homotopy equivalence;▫$\varepsilon$▫-map;cellular map;almost-smooth manifold;▫$|E_8|$▫-manifold;Kirby-Siebenmann class;Galewski-Stern obstruction;non-triangulable manifold;Alexandroff-Borsuk Manifold Problem;

Data

Language:	English
Year of publishing:	2017
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	515.12
COBISS:	17958233
ISSN:	0166-8641
Views:	488
Downloads:	321
Average score:	0 (0 votes)
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Other data

Secondary language:	Slovenian
Secondary title:	O problemu Aleksandrova in Borsuka
Secondary abstract:	We investigate the classical Alexandroff-Borsuk problem in the category of non-triangulable manifolds: Given an ▫$n$▫-dimensional compact non-triangulable manifold ▫$M^n$▫ and ▫$\varepsilon > 0$▫, does there exist an ▫$\varepsilon$▫-map of ▫$M^n$▫ onto an ▫$n$▫-dimensional finite polyhedron which induces a homotopy equivalence?
Secondary keywords:	ANR;končni polieder;homotopska ekvivalenca;▫$\varepsilon$▫-preslikava;celularna preslikava;skoraj gladka mnogoterost;$\|E_8\|$-mnogoterost;Kirby-Siebenmannov razred;Galewski-Sternova ovira;netriangulabilna mnogoterost;problem Aleksandrova in Borsuka o mnogoterostih;
Type (COBISS):	Article
Pages:	str. 114-120
Issue:	ǂVol. ǂ221
Chronology:	2017
DOI:	http://dx.doi.org/10.1016/j.topol.2017.02.052
ID:	11216351