Paper Title:

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

Published on:

2 October 2023

Primary Category:

K-Theory and Homology

Paper Authors:

Sherry Gong,

Jianchao Wu,

Zhizhang Xie,

Guoliang Yu

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Proves Novikov conjecture for discrete subgroups of diffeomorphism groups

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Removes volume-preserving condition from previous related work

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Uses operator K-theory and group actions on continuous fields of spaces

A simplified summary of key contributions

This paper proves the Novikov conjecture for a class of highly nonlinear groups, namely discrete subgroups of the diffeomorphism group of a compact smooth manifold. The key advance is removing the volume-preserving condition from previous work. The proof involves studying operator K-theory and group actions on continuous fields of infinite dimensional nonpositively curved spaces.

Higher index theory for extensions of finite groups

A more accessible title about the Teichmüller TQFT volume conjecture for the 7_3 knot

Non-rigidity of deformations of locally symmetric spaces

Large volume knots of fixed genus

Preimages stabilization for endomorphisms on projective lines

Differential Harnack inequality for noncompact hypersurfaces

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