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Metric geometry of locally compact groups

Author: Yves Cornulier; Pierre de La Harpe
Publisher: Zürich, Switzerland : European Mathematical Society Publishing House, ©2016.
Series: EMS tracts in mathematics, 25.; EMS tracts in mathematics, v. 25.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
(OCoLC)960090777
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Yves Cornulier; Pierre de La Harpe
ISBN: 9783037196663 3037196661
OCLC Number: 960788745
Notes: "Winnter of the 2016 EMS Monograph Award."
Description: 1 online resource (viii, 235 pages)
Contents: Basic properties --
Metric coarse and large-scale categories --
Groups as pseudo-metric spaces --
Examples of compactly generated LC-groups --
Coarse simple connectedness --
Bounded presentations --
Compactly presented groups.
Series Title: EMS tracts in mathematics, 25.; EMS tracts in mathematics, v. 25.
Responsibility: Yves Cornulier, Pierre de la Harpe.
More information:

Abstract:

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.

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