nLab Hantzsche-Wendt manifold




The Hantzsche-Wendt manifold (also called HW manifold or didicosm) is the coset space

DT 3/( 2× 2), D \coloneqq T^3/(\mathbb{Z}_2\times\mathbb{Z}_2) \,,

namely the quotient space of the 3-torus T 3T^3 by the antipodal action of 2× 2\mathbb{Z}_2\times\mathbb{Z}_2 on two components. It is a compact, orientable and flat 3-manifold.



The first and second amphidicosm are compact, non-orientable and flat 33-manifolds with holonomy group 2 2\mathbb{Z}_2^2 and first Betti number 11.

A generalized Hantzsche-Wendt manifold is a compact and flat nn-manifold with holonomy group 2 n1\mathbb{Z}_2^{n-1}.


First studied in:


On coverings:

  • Grigory Chelnokov and Alexander Mednykh, On the coverings of Hantzsche-Wendt manifold (2020), arXiv:2009.06691

Application in cosmic topology:

Explanation, visualisation and calculation of the first homology:

See also:

Last revised on June 10, 2024 at 15:26:22. See the history of this page for a list of all contributions to it.