Free groups acting without fixed points on rational spheres
For every positive rational number q, we find a free group of rotations of rank 2 acting on (√q𝕊²) ∩ ℚ³ whose all elements distinct from the identity have no fixed point.
For every positive rational number q, we find a free group of rotations of rank 2 acting on (√q𝕊²) ∩ ℚ³ whose all elements distinct from the identity have no fixed point.
We study the family of closed Riemannian n-manifolds with holonomy group isomorphic to Z2n-1, which we call generalized Hantzsche-Wendt manifolds. We prove results on their structure, compute some invariants, and find relations between them, illustrated in a graph connecting the family.