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:
Tipologija: 1.01 - Izvirni znanstveni članek
Organizacija: UL FMF - Fakulteta za matematiko in fiziko
UDK: 515.122
COBISS: 69890563 Povezava se bo odprla v novem oknu
ISSN: 0213-2230
Št. ogledov: 91
Št. prenosov: 43
Ocena: 0 (0 glasov)
Metapodatki: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

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