2010/02/17 by Thomas Koberda, Koberda, Thomas
Mathematics · Medicine · #20E26 (Primary) #Abelian group #Advanced Operator Algebra Research #Combinatorics #Corollary #FOS: Mathematics #Finitely-generated abelian group #Fundamental group #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Inflammatory Myopathies and Dermatomyositis #Manifold (fluid mechanics) #Mathematics #Nilpotent #Nilpotent group #Pure mathematics #Topology (electrical circuits) #Torsion (gastropod) #math.GR #math.GT #msc:20E26
paper · pdf · doi:10.48550/arxiv.1002.3203
Some changes made to improve readability and motivation and to correct typographical errors. The content is not changed
openalex publication_date 2010/02/17 · arxiv created 2010/02/19 · arxiv updated 2010/02/26 · openalex created_date 2025/10/24 · openalex updated_date 2026/08/05
In recent years, the RFRS condition has been used to analyze virtual fibering\nin 3-manifold topology. Agol's work shows that any 3-manifold with zero Euler\ncharacteristic satisfying the RFRS condition on its fundamental group virtually\nfibers over the circle. In this note we will show that a finitely generated\nnilpotent group is either virtually abelian or is not virtually RFRS, a result\nwhich may be of independent interest though not directly applicable to\n3-manifold topology. As a corollary, we deduce that any RFRS group cannot\ncontain a nonabelian torsion-free nilpotent group. This result also illustrates\nsome of the interplay between residual torsion-free nilpotence and the RFRS\ncondition.\n