Metric Geometry of Locally Compact Groups
This effective learning book offers the study of locally compact groups from the point of view of appropriate metrics to the students. Theory development in the book is supported by various examples including the matrix groups with the entries of real and complex numbers field. Book has been embellished with the study of locally compact fields such as p-adic, isometric groups of metric spaces and discrete groups.
Metric geometry of locally compact groups play major role but in particular case finitely generated groups were introduced in 1910 as connection with the word problem. The introduced some results exposed concern for the existence of compatible metrics and even results concerned with special classes of groups for instance mapping onto Z.
Before the application of general metric framework the basic notions of coarse and large scale geometry are developed in the general framework of metrics. Coarse geometry has been explained as part of geometry concerning properties of metric spaces that can be exemplified in terms of large distances.
In the book metric coarse equivalence, quasi isometrics of metric spaces, coarse simple connectedness are given special attention and the last chapters concentrate on the restricted class of compactly groups.