02585nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185100003000221245010700251260008200358300003400440336002600474337002600500338003600526347002400562490004000586506006600626520120000692650003401892650004201926650004001968650001802008650003802026700003402064856003202098856006902130209-160920CH-001817-320160920234502.0a fot ||| 0|cr nn mmmmamaa160920e20160930sz fot ||| 0|eng d a978303719666370a10.4171/1662doi ach0018173 7aPBFD2bicssc a20-xxa22-xxa51-xxa57-xx2msc1 aCornulier, Yves,eauthor.10aMetric Geometry of Locally Compact Groupsh[electronic resource] /cYves Cornulier, Pierre de la Harpe3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2016 a1 online resource (243 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v251 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php 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.07aGroups & group theory2bicssc07aGroup theory and generalizations2msc07aTopological groups, Lie groups2msc07aGeometry2msc07aManifolds and cell complexes2msc1 ade la Harpe, Pierre,eauthor.40uhttps://doi.org/10.4171/166423cover imageuhttps://www.ems-ph.org/img/books/cornulier_mini.jpg