The Novikov conjecture, the group of diffeomorphisms and continuous fields of Hilbert-Hadamard spaces
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866929724326936576 |
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| author | Gong, Sherry Wu, Jianchao Xie, Zhizhang Yu, Guoliang |
| author_facet | Gong, Sherry Wu, Jianchao Xie, Zhizhang Yu, Guoliang |
| contents | In this paper, we prove the Novikov conjecture for a class of highly non-linear groups, namely discrete subgroups of the diffeomorphism group of a compact smooth manifold. This removes the volume-preserving condition in a previous work. This result is proved by studying operator $K$-theory and group actions on continuous fields of infinite dimensional non-positively curved spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_01219 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Novikov conjecture, the group of diffeomorphisms and continuous fields of Hilbert-Hadamard spaces Gong, Sherry Wu, Jianchao Xie, Zhizhang Yu, Guoliang K-Theory and Homology Operator Algebras In this paper, we prove the Novikov conjecture for a class of highly non-linear groups, namely discrete subgroups of the diffeomorphism group of a compact smooth manifold. This removes the volume-preserving condition in a previous work. This result is proved by studying operator $K$-theory and group actions on continuous fields of infinite dimensional non-positively curved spaces. |
| title | The Novikov conjecture, the group of diffeomorphisms and continuous fields of Hilbert-Hadamard spaces |
| topic | K-Theory and Homology Operator Algebras |
| url | https://arxiv.org/abs/2310.01219 |