Free groups as end homogeneity groups of 3-manifolds

• Dennis J. Garity ^[1] ; Dušan D. Repovš ^[2]
  1. [1] Oregon State University

     Oregon State University

     Estados Unidos

     
  2. [2] University of Ljubljana

     University of Ljubljana

     Eslovenia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 1, 2022, págs. 113-130
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • For every finitely generated free group F, we construct an irreducible open 3-manifold MF whose end set is homeomorphic to a Cantor set, and with the end homogeneity group of MF 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 MG 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 R3 such that the graph automorphisms have certain nice extension properties, then there is an irreducible open 3-manifold MG with end homogeneity group G.