On the coverings of Hantzsche-Wendt manifold

DOI10.2748/tmj.20210308OpenAlexW3086594237MaRDI QIDQ2169417

Grigory R. Chelnokov, Alexander Mednykh

Publication date: 2 September 2022

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.06691

zbMATH Keywords

Dirichlet generating seriescrystallographic groupnumber of subgroupsplatycosmEuclidean formflat 3-manifoldnon-equivalent coveringsnumber of conjugacy classes of subgroups

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Covering spaces and low-dimensional topology (57M10) Other geometric groups, including crystallographic groups (20H15) Fiber bundles in algebraic topology (55R10)

Related Items

Cusps and commensurability classes of hyperbolic 4-manifolds ⋮ Seiberg-Witten Floer spectra and contact structures ⋮ Shift dynamics of the groups of Fibonacci type

Uses Software

• Bilbao Crystallography Server

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hearing the platycosms
• Counting conjugacy classes of subgroups in a finitely generated group.
• Hurwitz problem on the number of nonequivalent coverings of a compact Riemann surface
• Number of nonequivalent coverings over a nonorientable compact surface
• Fibonacci manifolds as two-fold coverings of the three-dimensional sphere and the Meyerhoff-Neumann conjecture
• 3-manifolds from Platonic solids.
• Subgroup growth.
• The enumeration of coverings of closed orientable Euclidean manifolds \(\mathcal{G}_3\) and \(\mathcal{G}_5\)
• On the Hantzsche-Wendt manifold
• On the coverings of Euclidean manifolds ℬ₁ and ℬ₂
• The Euclidean Representations of the Fibonacci Groups
• Enumeration of subgroups in the fundamental groups of orientable circle bundles over surfaces
• On the coverings of closed orientable Euclidean manifolds G2 and G4
• Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups
• Abelianization of space groups
• Sublattice enumeration. IV. Equivalence classes of plane sublattices by parent Patterson symmetry and colour lattice group type

This page was built for publication: On the coverings of Hantzsche-Wendt manifold