A Note on the Quasi Simple Filtration of Profinite Groups

Francesco G. Russo ()
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Francesco G. Russo: Mathematics Division, University of Camerino, School of Science and Technology

Chapter Chapter 15 in Essays on Topology, 2025, pp 311-326 from Springer

Abstract: Abstract We illustrate some intuitions of Poénaru (of more than 60 years ago) in connection with the property of quasi simple filtration, which was formulated later by Brick and Mihalik for finitely presented groups. This property adapts certain topological decompositions, which are proper to Low Dimensional Topology and Riemannian Geometry, to the context of Algebraic Topology, mostly to fundamental groups and universal coverings. We sketch some steps in the evolution of the property of quasi simple filtration, showing that there are significant margins of generalization to algebraic fundamental groups in theory of profinite groups.

Keywords: Geometric simple connectivity; Profinite groups; Algebraic fundamental groups; Etale; Primary: 20F05, 55M05; Secondary: 57M35, 57M40 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-81414-3_15

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DOI: 10.1007/978-3-031-81414-3_15

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