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

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arxiv 2310.01219 v3 pith:TMDGKILL submitted 2023-10-02 math.KT math.OA

Sherry Gong , Jianchao Wu , Zhizhang Xie , Guoliang Yu This is my paper · ORCID
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Embedding complexity into the universal Banach space and the strong Novikov conjecture

    math.FA 2026-05 unverdicted novelty 7.0 of 10

    The strong Novikov conjecture holds for countable discrete groups admitting a finite-complexity coarse embedding into an ℓ2-direct sum of property(H) Banach spaces.

  2. The Baum-Connes and the Mishchenko-Kasparov assembly maps for group extensions

    math.OA 2026-01 conditional novelty 7.0 of 10

    For group extensions, injectivity, surjectivity and isomorphism of the Baum-Connes assembly map, and rational injectivity of the Mishchenko-Kasparov map, pass from quotient and fiber pieces to the whole group under ex...

  3. Hilbert-Hadamard spaces and the equivariant coarse Novikov conjecture

    math.KT 2024-11 conditional novelty 7.0 of 10

    If a proper Γ-space with equivariant bounded geometry equivariantly and coarsely embeds into an admissible Hilbert-Hadamard space, then the rational analytic equivariant coarse Novikov conjecture holds.

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