Quantitative index, Novikov conjecture and coarse decomposability
K-Theory and Homology
2024-12-03 v1 Operator Algebras
Abstract
We define for families of finite metric spaces quantitative assembly map estimates that take into account propagation phenomena for pseudo-differential calculus. We relate these estimates to the Novikov conjecture and we show that they fit nicely under coarse decompositions. As an application, we provide a geometric proof of Novikov conjecture for groups with finite decomposition complexity.
Cite
@article{arxiv.2412.01314,
title = {Quantitative index, Novikov conjecture and coarse decomposability},
author = {Hervé Oyono-Oyono and Guoliang Yu},
journal= {arXiv preprint arXiv:2412.01314},
year = {2024}
}