Freedman, Michael H. \(\mathbb{Z}_2\)-systolic-freedom. (English) Zbl 1024.53029 Hass, Joel (ed.) et al., Proceedings of the Kirbyfest, Berkeley, CA, USA, June 22-26, 1998. Warwick: University of Warwick, Institute of Mathematics, Geom. Topol. Monogr. 2, 113-123 (1999). By a result of M. Gromov, stable systolic rigidity holds for any Riemannian metric on products of spheres \(S^p\times S^q\). The author investigates \({\mathbb Z}_2-\)systoles in dimensions bigger than or equal to three which are of relevance in quantum information theory. He shows that the conjectured systolic rigidity over \({\mathbb Z}_2\) does not hold. In fact, he exhibits a family of Riemannian metrics on \(S^2\times S^1\) showing up \({\mathbb Z}_2\)-\((2,1)\)-systolic freedom and leading to more general \( {\mathbb Z}_2\)-freedoms.For the entire collection see [Zbl 0939.00055]. Reviewer: Ruth Kellerhals (Fribourg) Cited in 3 Documents MSC: 53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces 53C22 Geodesics in global differential geometry 81P68 Quantum computation Keywords:systole; 3-manifold; torsion PDFBibTeX XMLCite \textit{M. H. Freedman}, Geom. Topol. Monogr. 2, 113--123 (1999; Zbl 1024.53029) Full Text: arXiv EMIS