Zhizhang Xie

activity

20102026

most citedOn the range of the relative higher index and the higher rho-invariant for positive scalar curvature

19 citations · 111 across the 40 of their papers we have counts for

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15 papers · 1 filter

math.KT2024

$ℓ^{p}$ -coarse Baum-Connes conjecture for $ℓ^{q}$ -coarse embeddable spaces

Jinmin Wang, Zhizhang Xie, Guoliang Yu +1

We prove an $ℓ^{p}$ -version of the coarse Baum-Connes conjecture for spaces that coarsely embedds into $ℓ^{q}$ -spaces for any $p$ and $q$ in $[1, \infty)$ .

math.KT2023

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

Sherry Gong, Jianchao Wu, Zhizhang Xie +1

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 rem…

math.KT2022

$l^{1}$ -higher index, $l^{1}$ -higher rho invariant and cyclic cohomology

Jinmin Wang, Zhizhang Xie, Guoliang Yu

In this paper, we study $l^{1}$ -higher index theory and its pairing with cyclic cohomology for both closed manifolds and compact manifolds with boundary. We first give a sufficient g…

math.KT2020★ 7 cited

Quantitative K-theory, positive scalar curvature, and band width

Hao Guo, Zhizhang Xie, Guoliang Yu

We develop two connections between the quantitative framework of operator $K$ -theory for geometric $C^{*}$ -algebras and the problem of positive scalar curvature. First, we introduce…

math.KT2020★ 3 cited

Functoriality for higher rho invariants of elliptic operators

Hao Guo, Zhizhang Xie, Guoliang Yu

Let $N$ be a closed spin manifold with positive scalar curvature and $D_{N}$ the Dirac operator on $N$ . Let $M_{1}$ and $M_{2}$ be two Galois covers of $N$ such that $M_{2}$ is a quotient…

math.KT2020★ 2 cited

Approximations of delocalized eta invariants by their finite analogues