On exactness and isoperimetric profiles of discrete groups
نویسندگان
چکیده
منابع مشابه
Amenable Actions and Exactness for Discrete Groups
It is proved that a discrete group G is exact if and only if its left translation action on the Stone-Čech compactification is amenable. Combining this with an unpublished result of Gromov, we have the existence of non exact discrete groups. In [KW], Kirchberg and Wassermann discussed exactness for groups. A discrete group G is said to be exact if its reduced group C-algebra C λ(G) is exact. Th...
متن کاملOn Isoperimetric Profiles and Computational Complexity
The isoperimetric profile of a graph is a function that measures, for an integer k, the size of the smallest edge boundary over all sets of vertices of size k. We observe a connection between isoperimetric profiles and computational complexity. We illustrate this connection by an example from communication complexity, but our main result is in algebraic complexity. We prove a sharp super-polyno...
متن کاملExactness of Locally Compact Groups
We give some new characterizations of exactness for locally compact second countable groups. In particular, we prove that a locally compact group is exact if and only if it admits a topologically amenable action on a compact Hausdorff space. This answers an open question by Anantharaman-Delaroche.
متن کاملDiscrete Isoperimetric Inequalities
One of the earliest problems in geometry is the isoperimetric problem, which was considered by the ancient Greeks. The problem is to find, among all closed curves of a given length, the one which encloses the maximum area. Isoperimetric problems for the discrete domain are in the same spirit but with different complexity. A basic model for communication and computational networks is a graph G =...
متن کاملcommuting and non -commuting graphs of finit groups
فرض کنیمg یک گروه غیر آبلی متناهی باشد . گراف جابجایی g که با نماد نمایش داده می شود ،گرافی است ساده با مجموعه رئوس که در آن دو راس با یک یال به هم وصل می شوند اگر و تنها اگر . مکمل گراف جابجایی g راگراف نا جابجایی g می نامیم.و با نماد نشان می دهیم. گرافهای جابجایی و ناجابجایی یک گروه متناهی ،اولین بار توسطاردوش1 مطرح گردید ،ولی در سالهای اخیر به طور مفصل در مورد بحث و بررسی قرار گرفتند . در ،م...
15 صفحه اولذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2007
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2006.10.011