Cornulier, Yves,
Metric Geometry of Locally Compact Groups [electronic resource] / Yves Cornulier, Pierre de la Harpe - Zuerich, Switzerland : European Mathematical Society Publishing House, 2016 - 1 online resource (243 pages) - EMS Tracts in Mathematics (ETM) 25 .
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
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.
9783037196663
10.4171/166 doi
Groups & group theory
Group theory and generalizations
Topological groups, Lie groups
Geometry
Manifolds and cell complexes
Metric Geometry of Locally Compact Groups [electronic resource] / Yves Cornulier, Pierre de la Harpe - Zuerich, Switzerland : European Mathematical Society Publishing House, 2016 - 1 online resource (243 pages) - EMS Tracts in Mathematics (ETM) 25 .
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
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.
9783037196663
10.4171/166 doi
Groups & group theory
Group theory and generalizations
Topological groups, Lie groups
Geometry
Manifolds and cell complexes