Torsion Obstructions to Positive Scalar Curvature
We study obstructions to the existence of Riemannian metrics of positive scalar curvature on closed smooth manifolds arising from torsion classes in the integral homology of their fundamental groups. As an application, we construct new examples of manifolds that do not admit positive scalar curvatur...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212351 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Torsion Obstructions to Positive Scalar Curvature. Misha Gromov and Bernhard Hanke. SIGMA 20 (2024), 069, 22 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862734657865383936 |
|---|---|
| author | Gromov, Misha Hanke, Bernhard |
| author_facet | Gromov, Misha Hanke, Bernhard |
| citation_txt | Torsion Obstructions to Positive Scalar Curvature. Misha Gromov and Bernhard Hanke. SIGMA 20 (2024), 069, 22 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study obstructions to the existence of Riemannian metrics of positive scalar curvature on closed smooth manifolds arising from torsion classes in the integral homology of their fundamental groups. As an application, we construct new examples of manifolds that do not admit positive scalar curvature metrics, but whose Cartesian products admit such metrics.
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| first_indexed | 2026-03-21T18:16:47Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212351 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T18:16:47Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Gromov, Misha Hanke, Bernhard 2026-02-05T09:55:47Z 2024 Torsion Obstructions to Positive Scalar Curvature. Misha Gromov and Bernhard Hanke. SIGMA 20 (2024), 069, 22 pages 1815-0659 2020 Mathematics Subject Classification: 53C21; 53C23; 20J06; 53C12; 55N10 arXiv:2112.04825 https://nasplib.isofts.kiev.ua/handle/123456789/212351 https://doi.org/10.3842/SIGMA.2024.069 We study obstructions to the existence of Riemannian metrics of positive scalar curvature on closed smooth manifolds arising from torsion classes in the integral homology of their fundamental groups. As an application, we construct new examples of manifolds that do not admit positive scalar curvature metrics, but whose Cartesian products admit such metrics. This paper is the result of conversations in New York in the fall of 2018 and 2022. B.H. acknowledges support from NYU, the IAS Princeton, and the DFG-funded Special Priority Program 2026 Geometry at Infinity. We are grateful to the referees for their many useful comments, which helped to improve the manuscript. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Torsion Obstructions to Positive Scalar Curvature Article published earlier |
| spellingShingle | Torsion Obstructions to Positive Scalar Curvature Gromov, Misha Hanke, Bernhard |
| title | Torsion Obstructions to Positive Scalar Curvature |
| title_full | Torsion Obstructions to Positive Scalar Curvature |
| title_fullStr | Torsion Obstructions to Positive Scalar Curvature |
| title_full_unstemmed | Torsion Obstructions to Positive Scalar Curvature |
| title_short | Torsion Obstructions to Positive Scalar Curvature |
| title_sort | torsion obstructions to positive scalar curvature |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212351 |
| work_keys_str_mv | AT gromovmisha torsionobstructionstopositivescalarcurvature AT hankebernhard torsionobstructionstopositivescalarcurvature |