Topics In Geometric Group Theory

Groups as abstract structures were first recognized by mathematicians in thenineteenth century. Groups are of course sets given with appropriatemultiplications ... » 

Groups as abstract structures were first recognized by mathematicians in thenineteenth century. Groups are of course sets given with appropriatemultiplications and they are often given together with actions oninteresting geometric objects. But groups are also interesting geometricobjects by themselves. More precisely a finitelygenerated group can be seenas a metric space the distance between two points being defined up to quasiisometry by some word length and this gives rise to a very fruitfulapproach to group theory.In this book Pierre de la Harpe provides a concise and engaging introductionto this approach a new method for studying infinite groups via their intrinsicgeometry that has played a major role in mathematics over the past two decades.A recognized expert in the field de la Harpe uses a handson presentationstyle illustrating key concepts of geometric group theory with numerousconcrete examples.The first five chapters present basic combinatorial and geometric group theoryin a unique way with an emphasis on finitelygenerated versus finitelypresented groups. In the final three chapters de la Harpe discusses newmaterial on the growth of groups including a detailed treatment of theGrigorchuk group an infinite finitelygenerated torsion group ofintermediate growth which is becoming more and more important in group theory.Most sections are followed by exercises and a list of problems and complementsenhancing the books value for students problems range from slightly moredifficult exercises to open research questions in the field. An extensive listof references directs readers to more advanced results as well asconnectionswith other subjects. «