Titlebook: Geometric Group Theory; An Introduction Clara Löh Textbook 2017 Springer International Publishing AG 2017 MSC 2010 20F65 20F67 20F69 20F05

Coronary

可互换

Cayley graphsA fundamental question of geometric group theory is how groups can be viewed as geometric objects; one way to view a (finitely generated) group as a geometric object is via Cayley graphs:

Affluence

Growth types of groupsThe first quasi-isometry invariant we discuss in detail is the growth type. We essentially measure the “volume” of balls in a given finitely generated group and study the asymptotic behaviour when the radius tends to infinity.

时代错误

冰雹

Amenable groupsThe notion of amenability revolves around the leitmotiv of (almost) invariance. Different interpretations of this leitmotiv lead to different characterisations of amenable groups, e.g., via invariant means, Følner sets (i.e., almost invariant finite subsets), decomposition properties, or fixed point properties.

险代理人

pacifist

Geometric Group Theory978-3-319-72254-2Series ISSN 0172-5939 Series E-ISSN 2191-6675

会犯错误

Trypsin

有害处

Definition of Drowning: A Progress Reportetric aspect of groups by looking at group actions, which can be viewed as a generalisation of seeing groups as symmetry groups.We start by recalling some basic concepts about group actions (Chapter 4.1).