Simply connected 3-manifolds with a dense set of ends of specified genus

Dennis Garity (Author), Dušan Repovš (Author)

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.

Keywords

3-manifold set;wild Cantor set;local genus;defining sequence;exhaustion;end;

Data

Language:	English
Year of publishing:	2017
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	515.124
COBISS:	18016345
ISSN:	1660-5446
Views:	507
Downloads:	338
Average score:	0 (0 votes)
Metadata:

Other data

Type (COBISS):	Article
Pages:	art. 109 (12 str.)
Volume:	ǂVol. ǂ14
Issue:	ǂiss. ǂ3
Chronology:	2017
DOI:	http://dx.doi.org/10.1007/s00009-017-0907-9
ID:	11215366