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Simply connected 3-manifolds with a dense set of ends of specified genus
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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
UDC:
515.124
ISSN on article:
1660-5446
DOI:
http://dx.doi.org/10.1007/s00009-017-0907-9
COBISS.SI-ID:
18016345
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
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