The R∞ property for crystallographic groups of Sol14

DOI10.1142/S0219498820500723zbMath1441.22015OpenAlexW2918454379WikidataQ114614694 ScholiaQ114614694MaRDI QIDQ5113145

Won Sok Yoo

Publication date: 2 June 2020

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219498820500723

zbMATH Keywords

Reidemeister number\( R_\infty\) property\(\text{Sol}_1^4\)crystallographic group of \(\text{Sol}_1^4\)

Mathematics Subject Classification ID

Nilpotent and solvable Lie groups (22E25) Fixed points and coincidences in algebraic topology (55M20) Other geometric groups, including crystallographic groups (20H15)

Cites Work

• Nielsen type numbers and homotopy minimal periods for maps on solvmanifolds with \(\operatorname{Sol}_{1}^{4}\)-geometry
• 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
• The finiteness of the Reidemeister number of morphisms between almost-crystallographic groups.
• Nielsen numbers of selfmaps of Sol 3-manifolds
• Aspects of the property \(R_\infty\).
• Nielsen type numbers and homotopy minimal periods for maps on the 3-nilmanifolds
• Twisted conjugacy classes in R. Thompson's group \(F\).
• Geometric structures on compact complex analytic surfaces
• The Reidemeister zeta function with applications to Nielsen theory and a connection with Reidemeister torsion
• The Reidemeister spectra of low dimensional crystallographic groups
• Nielsen type numbers and homotopy minimal periods for maps on 3-solvmanifolds
• A relationship between twisted conjugacy classes and the geometric invariants \(\Omega^n\).
• Groupoids and relations among Reidemeister and among Nielsen numbers
• The \(R_\infty\) property for crystallographic groups of Sol
• Crystallographic groups of Sol
• INFRA-SOLVMANIFOLDS OF Sol₁⁴
• Automorphisms of higher rank lamplighter groups
• Twisted conjugacy classes in nilpotent groups
• INFRA-SOLVMANIFOLDS OF TYPE (R)
• The $R_{\infty}$ property for Houghton's groups
• Averaging Formula for Nielsen Numbers

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