On positive scalar curvature bordism
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2019
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866929243459420160 |
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| author | Piazza, Paolo Schick, Thomas Zenobi, Vito Felice |
| author_facet | Piazza, Paolo Schick, Thomas Zenobi, Vito Felice |
| contents | Using standard results from higher (secondary) index theory, we prove that the positive scalar curvature bordism groups of a cartesian product GxZ are infinite in dimension 4n if n>0 G a group with non-trivial torsion. We construct representatives of each of these classes which are connected and with fundamental group GxZ. We get the same result in dimension 4n+2 (n>0) if G is finite and contains an element which is not conjugate to its inverse. This generalizes the main result of Kazaras, Ruberman, Saveliev, "On positive scalar curvature cobordism and the conformal Laplacian on end-periodic manifolds" to arbitrary even dimensions and arbitrary groups with torsion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_09168 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On positive scalar curvature bordism Piazza, Paolo Schick, Thomas Zenobi, Vito Felice Geometric Topology Differential Geometry K-Theory and Homology Using standard results from higher (secondary) index theory, we prove that the positive scalar curvature bordism groups of a cartesian product GxZ are infinite in dimension 4n if n>0 G a group with non-trivial torsion. We construct representatives of each of these classes which are connected and with fundamental group GxZ. We get the same result in dimension 4n+2 (n>0) if G is finite and contains an element which is not conjugate to its inverse. This generalizes the main result of Kazaras, Ruberman, Saveliev, "On positive scalar curvature cobordism and the conformal Laplacian on end-periodic manifolds" to arbitrary even dimensions and arbitrary groups with torsion. |
| title | On positive scalar curvature bordism |
| topic | Geometric Topology Differential Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/1912.09168 |