The finiteness of the Reidemeister number of morphisms between almost-crystallographic groups.

DOI10.1007/s11784-011-0043-2zbMath1237.20045OpenAlexW2005610511MaRDI QIDQ644438

Karel Dekimpe, Pieter Penninckx

Publication date: 4 November 2011

Published in: Journal of Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11784-011-0043-2

zbMATH Keywords

Reidemeister classesBieberbach groupsNielsen coincidence numbersReidemeister coincidence numbers

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Automorphisms of infinite groups (20E36) Fixed points and coincidences in algebraic topology (55M20) Other geometric groups, including crystallographic groups (20H15)

Related Items (15)

The \(R_\infty\) and \(S_\infty\) properties for linear algebraic groups ⋮ Formulas for the Reidemeister, Lefschetz and Nielsen coincidence number of maps between infra-nilmanifolds ⋮ Algorithms for twisted conjugacy classes of polycyclic-by-finite groups ⋮ Reidemeister zeta functions of low-dimensional almost-crystallographic groups are rational ⋮ The Reidemeister Spectra of Low Dimensional Almost-Crystallographic Groups ⋮ The R∞ property for crystallographic groups of Sol14 ⋮ Two examples related to the twisted Burnside-Frobenius theory for infinitely generated groups ⋮ Nielsen coincidence theory on infra-solvmanifolds of Sol ⋮ The Reidemeister spectra of low dimensional crystallographic groups ⋮ Coincidence theory for infra-nilmanifolds ⋮ Groupoids and relations among Reidemeister and among Nielsen numbers ⋮ The Nielsen and Reidemeister numbers of maps on infra-solvmanifolds of type \((\mathrm{R})\) ⋮ The \(R_\infty\) property for crystallographic groups of Sol ⋮ AVERAGING FORMULA FOR NIELSEN NUMBERS OF MAPS ON INFRA-SOLVMANIFOLDS OF TYPE (R) – CORRIGENDUM ⋮ HOMOTOPY MINIMAL PERIODS FOR HYPERBOLIC MAPS ON INFRA-NILMANIFOLDS

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