Exactness and uniform embeddability of discrete groups

积系统的C*-代数的有限维逼近

Finite-dimensional approximations for C*-algebras of product systems

研究积系统生成的C*-代数的精确性与核性，证明其等价于核或系数代数的相应性质，并指出紧对齐假设的必要性。

Exactness from Proper Actions

In this paper we show that if a discrete group $G$ acts properly isometrically on a discrete space $X$ for which the uniform Roe algebra $C_u^*(X)$ is exact then $G$ is an exact group. As a corollary, we note that if the action is cocompact then the following are equivalent: The space $X$ has Yu's property A; $C^*_u(X)$ is exact; $C_u^*(X)$ is nuclear.

群作用的$\mathrm{C}^*$-精确性与性质A

$\mathrm{C}^*$-exactness and property A for group actions

本文证明了离散群作用下的Schreier图具有性质A当且仅当其置换表示生成精确的$\mathrm{C}^*$-代数，从而推广了Cayley图的经典等价性和Sako关于一致Roe代数的定理。

Permanence properties of property A and coarse embeddability for locally compact groups

If $H$ is a lattice in a locally compact second countable group $G$, then we show that $G$ has property A (respectively is coarsely embeddable into Hilbert space) if and only if $H$ has property A (respectively is coarsely embeddable into Hilbert space). Moreover, we show three interesting generalizations of this result. If $H$ is a closed subgroup of $G$ that is co-amenable in $G$, and if $H$ has property A (respectively, is coarsely embeddable into Hilbert space), then we show that $G$ has property A (respectively, is coarsely embeddable into Hilbert space). We also show that an extension of…

Exactness and the Novikov Conjecture

We study the connection between the condition that the reduced C*-algebra of a finitely presented group is exact and the Novikov conjecture holding. The main result states that if the group is strongly exact in the sense that the inclusion of the group C*-algebra into the uniform Roe algebra of the group is a nuclear embedding then the Novikov conjecture holds for that group.

群体精确性与弱包含问题

Groupoid exactness and the weak containment problem

研究局部紧群体中精确性的类比，证明六个精确性概念的等价性，并探讨群体可接受性与C*-代数关系。