From the 1 of 9 linked papers with an AI index.
9 papers
Gromov's Simplicial Volume Vanishing Conjecture for Positive Scalar Curvature and Fundamental Group Decay
Qiaochu Ma, Guoliang Yu
The paper proves Gromov’s conjecture that closed oriented manifolds with positive scalar curvature have zero simplicial volume, assuming a mild decay condition on the fundamental g…
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…
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…
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.
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 -theoretic conjectures in noncommutative geometry. Motivated by the quest to verify Novikov-type conjec…
-coarse Baum-Connes conjecture for -coarse embeddable spaces
Jinmin Wang, Zhizhang Xie, Guoliang Yu +1
We prove an -version of the coarse Baum-Connes conjecture for spaces that coarsely embedds into -spaces for any and in .