On the Alexandroff-Borsuk problem

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

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?

• Language: English
• Keywords: ANR, 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
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2017
• Number of pages: Str. 114-120
• Numbering: Vol. 221
• PID: 20.500.12556/RUL-109543
• UDC: 515.12
• ISSN on article: 0166-8641
• DOI: http://dx.doi.org/10.1016/j.topol.2017.02.052
• COBISS.SI-ID: 17958233
• Publication date in RUL: 05.09.2019

Record is a part of a journal

• Title: Topology and its Applications
• Shortened title: Topol. appl.
• Publisher: North-Holland
• ISSN: 0166-8641
• COBISS.SI-ID: 26538752

Secondary language

• Language: Slovenian
• Title: O problemu Aleksandrova in Borsuka

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