Positive Scalar Curvature and crystallographic fundamental groups
Algebraic Topology
2025-03-24 v2 Differential Geometry
Group Theory
Abstract
We examine positive and negative results for the Gromov-Lawson-Rosenberg Conjecture within the class of crystallographic groups. We give necessary conditions within the class of split extensions of free abelian by cyclic groups to satisfy the unstable Gromov-Lawson-Rosenberg Conjecture. We also give necessary conditions within the same class of groups, producing an infinite number of counterexamples for the conjecture.
Keywords
Cite
@article{arxiv.2503.11931,
title = {Positive Scalar Curvature and crystallographic fundamental groups},
author = {Noe Barcenas and Mario Velasquez},
journal= {arXiv preprint arXiv:2503.11931},
year = {2025}
}