Profinite genus of fundamental groups of compact flat manifolds with the cyclic holonomy group of square-free order

2021/02/02 by Genildo de Jesus Nery, Nery, Genildo de Jesus · 1 citation
Mathematics · #Geometric and Algebraic Topology #Geometry and complex manifolds #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2102.01762

Abstract

In this article we study the extent to which an n-dimensional compact flat manifold with the cyclic holonomy group of square-free order may be distinguished by the finite quotients of its fundamental group. In particular, we display a formula for the cardinality of profinite genus of the fundamental group of an n-dimensional compact flat manifold with the cyclic holonomy group of square-free order.

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• The profinite genus of the groups ℤⁿ\rtimes C_p²

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