The groups Aut and Out of the fundamental group of a closed Sol 3-manifold

Author(s)

Goncalves, Daciberg Lima ; Martins, Sergio Tadao

• Document type: Journal article
• Source: JOURNAL OF ALGEBRA AND ITS APPLICATIONS; v. N/A, p. 29-pg., 2022-07-07.

Abstract

Let E be the fundamental group of a closed Sol 3-manifold. We describe the groups Aut(E) and Out(E). We first consider the case where E is the fundamental group of a torus bundle, and then the case where E is the fundamental group of a closed Sol 3-manifold which is not a torus bundle. The groups are described in terms of some iterated semidirect products of well-known groups, where one exception is for Out(E) for some E's, in which case Out(E) is described as an extension and a presentation is given. (AU)

• FAPESP's process: 16/24707-4 - Algebraic, geometric and differential topology
• Grantee: Daciberg Lima Gonçalves
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 12/24454-8 - Algebraic, geometric and differential topology
• Grantee: Daciberg Lima Gonçalves
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 13/07510-4 - Resolutions and the group cohomology of the sapphire manifolds and of the virtually cyclic groups
• Grantee: Sérgio Tadao Martins
• Support Opportunities: Scholarships in Brazil - Post-Doctoral