Computation of Five-and Six-Dimensional Bieberbach Groups

DOI10.1080/10586458.2001.10504433zbMath0980.20043OpenAlexW2024898652MaRDI QIDQ2729383

Carlos Cid, Tilman Schulz

Publication date: 22 July 2001

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/999188425

zbMATH Keywords

holonomy groupscrystallographic groupsBieberbach groups

Mathematics Subject Classification ID

Topological methods in group theory (57M07) Other geometric groups, including crystallographic groups (20H15) Software, source code, etc. for problems pertaining to group theory (20-04)

Related Items (11)

Counting Crystallographic Groups in Low Dimensions ⋮ Teichmüller theory and collapse of flat manifolds ⋮ The action of matrix groups on aspherical manifolds ⋮ \({\mathbb{Z}}_2^k\)-manifolds are isospectral on forms ⋮ Topological and affine classification of complete noncompact flat 4-manifolds ⋮ \(\mathbb Z_2\)-cohomology and spectral properties of flat manifolds of diagonal type ⋮ Parallel spinors on flat manifolds ⋮ Generalized Hantzsche-Wendt flat manifolds. ⋮ The eta invariant and equivariant bordism of flat manifolds with cyclic holonomy group of odd prime order ⋮ Kähler flat manifolds ⋮ The eta function and eta invariant of \(\mathbb{Z}_{2^r}\)-manifolds

Uses Software

• GAP
• CARAT

Cites Work

• Unnamed Item
• On the holonomy group of locally euclidean spaces
• Five dimensional Bieberbach groups with trivial centre
• Holonomy groups of five dimensional Bieberbach groups
• Über einen Algorithmus zur Bestimmung der Raumgruppen
• Crystallographic Algorithms and Tables
• HOLONOMY OF FLAT MANIFOLDS WITH b₁ = 0
• Counting Crystallographic Groups in Low Dimensions

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