Contractible 3-manifolds and the double 3-space property

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

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.

• Language: English
• Keywords: contractible 3-manifold, open 3-manifold, Whitehead Link, defining sequence, geometric index, McMillan contractible 3-manifold, Gabai Link
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2018
• Number of pages: Str. 2039-2055
• Numbering: Vol. 370, no. 3
• PID: 20.500.12556/RUL-109014
• UDC: 515.124.5
• ISSN on article: 0002-9947
• DOI: 10.1090/tran/7035
• COBISS.SI-ID: 18165593

Note

Članek je bil izbran med dosežke Odlični v znanosti 2018 (http://www.arrs.si/sl/analize/publ/inc/19/ARRS-LP-18.pdf)

• Publication date in RUL: 19.08.2019

Record is a part of a journal

• Title: Transactions of the American Mathematical Society
• Shortened title: Trans. Am. Math. Soc.
• Publisher: American Mathematical Society.
• ISSN: 0002-9947
• COBISS.SI-ID: 435213