Guoliang Yu

activity

20192026

most citedQuantitative index, Novikov conjecture and coarse decomposability

22 citations · 24 across the 11 of their papers we have counts for

collaborators

14 papers

math.KT2026

Classifying quasi-representations of groups via their characters

Shmuel Weinberger, Jianchao Wu, Guoliang Yu

For every countable discrete group, we construct a character for finite-dimensional unitary quasi-representations, with values in the inverse limit of the equivariant $K$ -theory of…

math.DG2026

Gromov's dihedral rigidity conjecture in dimension three

Jinmin Wang, Zhizhang Xie, Guoliang Yu

In this article, we present a self-contained proof of Gromov's dihedral rigidity conjecture on scalar curvature in the three-dimensional case. The proof avoids many of the technica…

math.DG2026

Gromov's Simplicial Volume Vanishing Conjecture for Positive Scalar Curvature

Qiaochu Ma, Jinmin Wang, Zhizhang Xie +2

In this paper, we prove Gromov's simplicial volume vanishing conjecture for closed manifolds with spin universal cover. More precisely, we show that if a closed oriented manifold a…

math.DG2025

Small scale index theory, scalar curvature, and Gromov's simplicial norms

Qiaochu Ma, Guoliang Yu

In this article, we study the topological complexity of manifolds with a lower scalar curvature bound. We introduce a small scale index theorem to establish an upper bound for Grom…

math.KT2024★ 22 cited

Quantitative index, Novikov conjecture and coarse decomposability

Hervé Oyono-Oyono, Guoliang Yu

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 es…

math.AT2024

Equivalence of different definitions of higher $ρ$ invariants

Hongzhi Liu, Zhizhang Xie, Guoliang Yu

For each orientation-preserving homotopy equivalence between two closed oriented smooth manifolds, there are mainly two different approaches to the higher $ρ$ invariant associated…

math.KT2024

Hilbert-Hadamard spaces and the equivariant coarse Novikov conjecture

Liang Guo, Qin Wang, Jianchao Wu +1

The equivariant coarse Novikov conjectures stand among a handful profound $K$ -theoretic conjectures in noncommutative geometry. Motivated by the quest to verify Novikov-type conjec…

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.DG2024

Bounding the A-hat genus using scalar curvature lower bounds and isoperimetric constants

Qiaochu Ma, Jinmin Wang, Guoliang Yu +1

In this paper, we prove an upper bound on the $A$ genus of a smooth, closed, spin Riemannian manifold using its scalar curvature lower bound, Neumann isoperimetric consta…

math.KT2023

Higher index theory for spaces with an FCE-by-FCE structure

Jintao Deng, Liang Guo, Qin Wang +1

Let $(1 \to N_{n} \to G_{n} \to Q_{n} \to 1)_{n \in N}$ be a sequence of extensions of finite groups. Assume that the coarse disjoint unions of $(N_{n})_{n \in N}$ , $(G_n)_{n \…

math.DG2023

Filling Radius, Quantitative $K$ -theory and Positive Scalar Curvature

Jinmin Wang, Zhizhang Xie, Guoliang Yu +1

We prove a quantitative upper bound on the filling radius of complete, spin manifolds with uniformly positive scalar curvature using the quantitative operator $K$ -theory and index…

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.FA2023

Strong relative Novikov conjecture for coarsely embeddable groups

Geng Tian, Zhizhang Xie, Guoliang Yu

In this article, we prove a strong relative Novikov conjecture for any pair of groups that are coarsely embeddable into Hilbert space.

math.GT2019★ 2 cited

The Novikov Conjecture