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arXiv · 2503.11931

Positive Scalar Curvature and crystallographic fundamental groups

Noe Barcenas·Mario Velasquez
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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.

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Noe Barcenas, Mario Velasquez. 2025-03-15. Positive Scalar Curvature and crystallographic fundamental groups. https://arxiv.org/abs/2503.11931

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