Free groups as end homogeneity groups of 3-manifolds

Dennis Garity (Author), Dušan Repovš (Author)

Abstract

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 ▫$G$▫.

Keywords

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

Data

Language:	English
Year of publishing:	2022
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	515.122
COBISS:	69890563
ISSN:	0213-2230
Views:	91
Downloads:	43
Average score:	0 (0 votes)
Metadata:

Other data

Type (COBISS):	Article
Pages:	str. 113-130
Volume:	ǂVol. ǂ38
Issue:	ǂiss. ǂ1
Chronology:	2022
DOI:	10.4171/RMI/1273
ID:	14696213