LEADER 03031nam 22005055a 450 001 9910153279303321 005 20220606185949.0 010 $a3-03719-666-1 024 70$a10.4171/166 035 $a(CKB)3580000000002053 035 $a(CH-001817-3)209-160920 035 $a(PPN)195294017 035 $a(EXLCZ)993580000000002053 100 $a20160920j20160930 fy 0 101 0 $aeng 135 $aurnn#mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMetric geometry of locally compact groups$b[electronic resource] /$fYves Cornulier, Pierre de la Harpe 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2016 215 $a1 online resource (243 pages) 225 0 $aEMS Tracts in Mathematics (ETM)$v25 311 $a3-03719-166-X 327 $aBasic 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. 330 $aWinner 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. 606 $aGroups & group theory$2bicssc 606 $aGroup theory and generalizations$2msc 606 $aTopological groups, Lie groups$2msc 606 $aGeometry$2msc 606 $aManifolds and cell complexes$2msc 615 07$aGroups & group theory 615 07$aGroup theory and generalizations 615 07$aTopological groups, Lie groups 615 07$aGeometry 615 07$aManifolds and cell complexes 676 $a512.2 686 $a20-xx$a22-xx$a51-xx$a57-xx$2msc 700 $aCornulier$b Yves$01071025 702 $ade la Harpe$b Pierre 801 0$bch0018173 906 $aBOOK 912 $a9910153279303321 996 $aMetric Geometry of Locally Compact Groups$92565672 997 $aUNINA