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

Dennis Garity (Avtor), Dušan Repovš (Avtor)

Povzetek

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.

Ključne besede

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

Podatki

Jezik:	Angleški jezik
Leto izida:	2017
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL FMF - Fakulteta za matematiko in fiziko
UDK:	515.124
COBISS:	18016345
ISSN:	1660-5446
Št. ogledov:	507
Št. prenosov:	338
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Vrsta dela (COBISS):	Članek v reviji
Strani:	art. 109 (12 str.)
Letnik:	ǂVol. ǂ14
Zvezek:	ǂiss. ǂ3
Čas izdaje:	2017
DOI:	http://dx.doi.org/10.1007/s00009-017-0907-9
ID:	11215366