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Simply connected 3-manifolds with a dense set of ends of specified genus
ID Garity, Dennis (Author), ID Repovš, Dušan (Author)

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Abstract
We show that for every sequence ▫$(n_i)$▫, where each ▫$n_i$▫ is either an integer greater than 1 or is ▫$\infty$▫, there exists a simply connected open 3-manifold ▫$M$▫ with a countable dense set of ends ▫$\{e_i\}$▫ so that, for every ▫$i$▫, the genus of end ▫$e_i$▫ is equal to ▫$n_i$▫. In addition, the genus of the ends not in the dense set is shown to be less than or equal to 2. These simply connected 3-manifolds are constructed as the complements of certain Cantor sets in ▫$S^3$▫. The methods used require careful analysis of the genera of ends and new techniques for dealing with infinite genus.

Language:English
Keywords:3-manifold set, wild Cantor set, local genus, defining sequence, exhaustion, end
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:12 str.
Numbering:art. 109, iss. 3
PID:20.500.12556/RUL-109515 This link opens in a new window
UDC:515.124
ISSN on article:1660-5446
DOI:http://dx.doi.org/10.1007/s00009-017-0907-9 This link opens in a new window
COBISS.SI-ID:18016345 This link opens in a new window
Publication date in RUL:04.09.2019
Views:870
Downloads:480
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Record is a part of a journal

Title:Mediterranean journal of mathematics
Shortened title:Mediterr. j. math.
Publisher:Springer Nature, Birkhäuser
ISSN:1660-5446
COBISS.SI-ID:13561433 This link opens in a new window

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