Dennis Garity (Author), Dušan Repovš (Author), David Wright (Author)

Abstract

Gabai showed that the Whitehead manifold is the union of two submanifolds each of which is homeomorphic to ▫$\mathbb{R}^3$▫ and whose intersection is again homeomorphic to ▫$\mathbb{R}^3$▫. Using a family of generalizations of the Whitehead Link, we show that there are uncountably many contractible 3-manifolds with this double 3-space property. Using a separate family of generalizations of the Whitehead Link and using an extension of interlacing theory, we also show that there are uncountably many contractible 3-manifolds that fail to have this property.

Keywords

contractible 3-manifold;open 3-manifold;Whitehead Link;defining sequence;geometric index;McMillan contractible 3-manifold;Gabai Link;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 515.124.5
COBISS: 18165593 Link will open in a new window
ISSN: 0002-9947
Views: 461
Downloads: 245
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Other data

Type (COBISS): Article
Source comment: Članek je bil izbran med dosežke Odlični v znanosti 2018 (http://www.arrs.si/sl/analize/publ/inc/19/ARRS-LP-18.pdf)
Pages: str. 2039-2055
Volume: ǂVol. ǂ370
Issue: ǂno. ǂ3
Chronology: March 2018
DOI: 10.1090/tran/7035
ID: 11204074