Ends of Groups
Nic Koban, John Meier · Princeton University Press eBooks · 2017
This chapter focuses on the ends of a group. It first constructs a group action on the Cantor set and creates a free group from bijections of the Cantor set before showing how the idea of trying to understand what is happening at infinity for an infinite group is captured by the phrase “the ends of a group.” It then explores the notion of ends in the context of infinite graphs and presents examples that provide some insight into the number of ends of groups. It also looks at semidirect products and demonstrates how to calculate the number of ends of the braid groups before moving beyond the process of counting the ends of a group, taking into account the ends of the 4-valent tree. The discussion includes exercises and research projects.