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Metric Geometry of Locally Compact Groups
EMS Tracts in Mathematics Vol. 25

Yves Cornulier (Université Paris-Sud, Orsay, France)
Pierre de la Harpe (Université de Genève, Switzerland)

Metric Geometry of Locally Compact Groups

ISBN print 978-3-03719-166-8, ISBN online 978-3-03719-666-3
DOI 10.4171/166
September 2016, 243 pages, hardcover, 17 x 24 cm.
62.00 Euro

Winner of the 2016 EMS Monograph Award!

The main aim of this book is the study of locally compact groups from a geometric perspective, with an emphasis on appropriate metrics that can be defined on them. The approach has been successful for finitely generated groups, and can favourably be extended to locally compact groups. Parts of the book address the coarse geometry of metric spaces, where ‘coarse’ refers to that part of geometry concerning properties that can be formulated in terms of large distances only. This point of view is instrumental in studying locally compact groups.

Basic results in the subject are exposed with complete proofs, others are stated with appropriate references. Most importantly, the development of the theory is illustrated by numerous examples, including matrix groups with entries in the the field of real or complex numbers, or other locally compact fields such as p-adic fields, isometry groups of various metric spaces, and, last but not least, discrete group themselves.

The book is aimed at graduate students and advanced undergraduate students, as well as mathematicians who wish some introduction to coarse geometry and locally compact groups.

Keywords: Locally compact groups, left-invariant metrics, $\sigma$-compactness, second countability, compact generation, compact presentation, metric coarse equivalence, quasi-isometry, coarse connectedness, coarse simple connectedness, growth, amenability