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arXiv · 2310.01219

The Novikov conjecture, the group of diffeomorphisms and continuous fields of Hilbert-Hadamard spaces

Sherry Gong·Jianchao Wu·Zhizhang Xie·Guoliang Yu
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Abstract

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.

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Sherry Gong, Jianchao Wu, Zhizhang Xie, Guoliang Yu. 2023-10-02. The Novikov conjecture, the group of diffeomorphisms and continuous fields of Hilbert-Hadamard spaces. https://arxiv.org/abs/2310.01219

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