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Topics in Geometric Group Theory (Paperback, 2nd Ed.)
Loot Price: R1,254
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Topics in Geometric Group Theory (Paperback, 2nd Ed.)
Series: Chicago Lectures in Mathematics Series CLM (CHUP)
Expected to ship within 12 - 17 working days
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Groups as abstract structures were first recognized by
mathematicians in the nineteenth century. Groups are, of course,
sets given with appropriate "multiplications," and they are often
given together with actions on interesting geometric objects. But
groups are also interesting geometric objects by themselves. More
precisely, a finitely-generated group can be seen as a metric
space, the distance between two points being defined "up to
quasi-isometry" by some "word length," and this gives rise to a
very fruitful approach to group theory.
In this book, Pierre de la Harpe provides a concise and engaging
introduction to this approach, a new method for studying infinite
groups via their intrinsic geometry that has played a major role in
mathematics over the past two decades. A recognized expert in the
field, de la Harpe uses a hands-on presentation style, illustrating
key concepts of geometric group theory with numerous concrete
examples.
The first five chapters present basic combinatorial and geometric
group theory in a unique way, with an emphasis on
finitely-generated versus finitely-presented groups. In the final
three chapters, de la Harpe discusses new material on the growth of
groups, including a detailed treatment of the "Grigorchuk group,"
an infinite finitely-generated torsion group of intermediate growth
which is becoming more and more important in group theory. Most
sections are followed by exercises and a list of problems and
complements, enhancing the book's value for students; problems
range from slightly more difficult exercises to open research
questions in the field. An extensive list of references directs
readers to more advanced results as well as connectionswith other
subjects.
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