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Noe Barcenas and
Mario Velasquez
Positive scalar curvature and crystallographic fundamental groups
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| Published: |
May 3, 2026. |
| Keywords: |
Gromov-Lawson-Rosenberg Conjecture, Group homology, (connective) topological K-theory, extensions of Zn by Z/m. |
| Subject [2020]: |
46L80, 53C27. |
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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 which are counterexamples for the conjecture.
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| Acknowledgements
The first named author aknowledges support of DGAPA-PAPIIT Grant IN101423. Both authors thank the exchange program CIC-UNAM.
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| Author information
Noe Barcenas
Centro de Ciencias Matematicas
UNAM \\Ap.Postal 61-3 Xangari
Morelia, Michoacan 58089, MEXICO
barcenas@matmor.unam.mx
Mario Velasquez
Universidad Nacional de Colombia Sede Bogota
Departamento de Matematicas
Facultad de Ciencias
Cra. 30 cll 45 - Ciudad Universitaria, Bogota, Colombia
mavelasquezme@unal.edu.co
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