Topology of 3-manifolds and a class of groups

2002/09/11 by S. K. Roushon, S.K. Roushon, Roushon, S. K. · 1 citation
Computer Science · Mathematics · #57M99. Secondary: 20E99 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Primary: 20F19 #Topological and Geometric Data Analysis #math.GR #math.GT #msc:20E99 #msc:20F19 #msc:57M99.

paper · pdf · doi:10.48550/arxiv.math/0209121

13 pages. Revised version with some new results and corrections

openalex publication_date 2002/09/11 · arxiv created 2002/11/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper grew out of an attempt to find a suitable finite sheeted covering of an aspherical 3-manifold so that the cover either has infinite or trivial first homology group. With this motivation we define a new class of groups. These groups are in some sense eventually perfect. We prove results giving several classes of examples of groups which do (not) belong to this class. Also we prove some elementary results on these groups and state two conjectures. A direct application of one of the conjectures to the virtual Betti number conjecture of Thurston is mentioned.

Cited by

• L-theory of groups with unstable derived series

Related

• Three-manifolds class field theory (Homology of coverings for a non-virtually Haken manifold)
• Compactifying sufficiently regular covering spaces of compact\n 3-manifolds
• 3-manifold groups
• Some 3-manifold groups with the same finite quotients
• A challenge to 3-manifold topologists and group algebraists