Groups and Their Actions

J.C. Álvarez Paiva

In this first chapter we study linear groups and their actions. We concentrate on those transitive actions and homogeneous spaces which are ubiquitous in geometry.

Notes

• Anything preceded by a * may be left for a second reading.

• Next to the exercises there is a two-digit number in parentheses which describes its degree of difficulty. The simplest exercises are identified by a (00), while the hardest -- those that could take you a week of intensive brain work -- are identified by a (50).