论文标题
配备双不可变化的基团的定向渐近锥
Directional asymptotic cones of groups equipped with bi-invariant metrics
论文作者
论文摘要
鉴于一个组上的双重变量度量，我们在不使用超滤器的情况下构建了渐近锥的版本。该新结构称为定向渐近锥，是一个配备完整的双重不变度量的合同拓扑组，并承认标准渐近锥的规范同构同构。此外，可数基团的定向渐近锥可分开。
Given a bi-invariant metric on a group, we construct a version of an asymptotic cone without using ultrafilters. The new construction, called the directional asymptotic cone, is a contractible topological group equipped with a complete bi-invariant metric and admits a canonical Lipschitz homomorphism to the standard asymptotic cone. Moreover, the directional asymptotic cone of a countable group is separable.
