Profinite genus of fundamental groups of torus bundles

2018/11/17 by Nery, Genildo de Jesus · 1 citation
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1811.07202

Abstract

In this paper we establish lower and upper bounds for the cardinality of the profinite genus of the fundamental group π₁(M_A)≅ (ℤ × ℤ)\rtimes_Aℤ of a torus bundle M_A in terms of the number of ideal classes of the order ℤ[λ], where λ is an eigenvalue of the matrix A in GL₂(ℤ).

Cited by

• The profinite genus of the groups ℤⁿ\rtimes C_p²

Related

• Profinite genus of fundamental groups of compact flat manifolds with holonomy group of prime order
• Profinite genus of fundamental groups of compact flat manifolds with the cyclic holonomy group of square-free order
• The profinite genus of the groups ℤⁿ\rtimes C_p²
• Explicit Computations of Fundamental Classes
• Variations on a theme of Grothendieck