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

2023/10/02 by Gong, Sherry, Wu, Jianchao, Xie, Zhizhang +1
#FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2310.01219

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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