Reidemeister zeta functions of low-dimensional almost-crystallographic groups are rational

DOI10.1080/00927872.2018.1435792zbMath1473.20055arXiv1710.02335OpenAlexW2761623846MaRDI QIDQ4576729

Iris van den Bussche, Sam Tertooy, Karel Dekimpe

Publication date: 10 July 2018

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.02335

zbMATH Keywords

zeta functiontwisted conjugacyalmost-crystallographic groupReidemeister number

Mathematics Subject Classification ID

Other geometric groups, including crystallographic groups (20H15) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Related Items (5)

Pólya-Carlson dichotomy for coincidence Reidemeister zeta functions via profinite completions ⋮ New zeta functions of Reidemeister type and the twisted Burnside-Frobenius theory ⋮ Dynamical zeta functions of Reidemeister type and representations spaces ⋮ Dynamical zeta functions of Reidemeister type ⋮ The Reidemeister spectra of low dimensional crystallographic groups

Cites Work

• Nielsen zeta functions for maps on infra-nilmanifolds are rational
• The finiteness of the Reidemeister number of morphisms between almost-crystallographic groups.
• Bieberbach groups and flat manifolds
• The Nielsen and Reidemeister numbers of maps on infra-solvmanifolds of type \((\mathrm{R})\)
• Almost-Bieberbach groups: affine and polynomial structures
• Geometry of Crystallographic Groups
• Lectures on Nielsen fixed point theory
• Dynamical zeta functions, Nielsen theory and Reidemeister torsion

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