Equivalence of different definitions of higher $ρ$ invariants

Hongzhi Liu, Zhizhang Xie, Guoliang Yu

Published 2024-11-22Version 1

For each orientation-preserving homotopy equivalence between two closed oriented smooth manifolds, there are mainly two different approaches to the higher $\rho$ invariant associated to this homotopy equivalence. In this article, we show that these two definitions of the higher $\rho$ invariant are equivalent.