Free groups as end homogeneity groups of 3-manifolds

Dennis Garity (Avtor), Dušan Repovš (Avtor)

Povzetek

For every finitely generated free group ▫$F$▫, we construct an irreducible open 3-manifold ▫$M_F$▫ whose end set is homeomorphic to a Cantor set, and with the end homogeneity group of ▫$M_F$▫ isomorphic to ▫$F$▫. The end homogeneity group is the group of all self-homeomorphisms of the end set that extend to homeomorphisms of the entire 3-manifold. This extends an earlier result that constructs, for each finitely generated abelian group ▫$G$▫, an irreducible open 3-manifold ▫$M_G$▫ with end homogeneity group ▫$G$▫. The method used in the proof of our main result also shows that if ▫$G$▫ is a group with a Cayley graph in ▫$\mathbb{R}^3$▫ such that the graph automorphisms have certain nice extension properties, then there is an irreducible open 3-manifold ▫$M_G$▫ with end homogeneity group ▫$G$▫.

Ključne besede

open 3-manifold;rigidity;manifold end;geometric index;Cantor set;homogeneity group;abelian group;defining sequence;

Podatki

Jezik:	Angleški jezik
Leto izida:	2022
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL FMF - Fakulteta za matematiko in fiziko
UDK:	515.122
COBISS:	69890563
ISSN:	0213-2230
Št. ogledov:	91
Št. prenosov:	43
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Vrsta dela (COBISS):	Članek v reviji
Strani:	str. 113-130
Letnik:	ǂVol. ǂ38
Zvezek:	ǂiss. ǂ1
Čas izdaje:	2022
DOI:	10.4171/RMI/1273
ID:	14696213