Profinite genus of fundamental groups of compact flat manifolds with holonomy group of prime order

DOI10.1515/JGTH-2020-0175arXiv2006.11810MaRDI QIDQ6343388

Genildo de Jesus Nery

Publication date: 21 June 2020

Abstract: In this article we calculate the profinite genus of the fundamental group of a $n$-dimensional compact flat manifold $X$ with holonomy group of prime order. As consequence, we prove that if $nleq21$, then $X$ is determined among all $n$-dimensional compact flat manifolds by the profinite completion of its fundamental group. Furthermore, we characterize the isomorphism class of profinite completion of the fundamental group of $X$ in terms of the representation genus of its holonomy group.

Mathematics Subject Classification ID

Fundamental group, presentations, free differential calculus (57M05) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34) Limits, profinite groups (20E18)

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