Spin$^c$ structures on Hantzsche-Wendt manifolds
Rafa{\l} Lutowski, Jerzy Popko, Andrzej Szczepa\'nski
TL;DR
This paper proves that all Hantzsche-Wendt manifolds of dimension greater than three do not admit spin$^c$ structures, using combinatorial methods to analyze their Stiefel-Whitney classes.
Contribution
It provides a combinatorial approach to determine the non-existence of spin$^c$ structures on higher-dimensional Hantzsche-Wendt manifolds, extending previous knowledge.
Findings
No Hantzsche-Wendt manifold of dimension > 3 admits a spin$^c$ structure.
Utilizes combinatorial description of Stiefel-Whitney classes.
Establishes a dimension threshold for the existence of spin$^c$ structures.
Abstract
Using a combinatorial description of Stiefel-Whitney classes of closed flat manifolds with diagonal holonomy representation, we show that no Hantzsche-Wendt manifold of dimension greater than three does not admit a spin structure.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology