Equivalence of different definitions of higher $\rho$ invariants

Hongzhi Liu; Zhizhang Xie; Guoliang Yu

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arXiv · 2411.16716

Equivalence of different definitions of higher $\rho$ invariants

Hongzhi Liu·Zhizhang Xie·Guoliang Yu

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Abstract

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.

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Hongzhi Liu, Zhizhang Xie, Guoliang Yu. 2024-11-22. Equivalence of different definitions of higher $\rho$ invariants. https://arxiv.org/abs/2411.16716

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