02184nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084001500185100002700200245010800227260008200335300003400417336002600451337002600477338003600503347002400539490005100563506006600614520099200680650003401672650004201706856003201748856006601780234-180509CH-001817-320180509233001.0a fot ||| 0|cr nn mmmmamaa180509e20180525sz fot ||| 0|eng d a978303719689270a10.4171/1892doi ach0018173 7aPBFD2bicssc a20-xx2msc1 aThomas, Anne,eauthor.10aGeometric and Topological Aspects of Coxeter Groups and Buildingsh[electronic resource] /cAnne Thomas3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2018 a1 online resource (160 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aCoxeter groups are groups generated by reflections, and they appear throughout mathematics. Tits developed the general theory of Coxeter groups in order to develop the theory of buildings. Buildings have interrelated algebraic, combinatorial and geometric structures, and are powerful tools for understanding the groups which act on them. These notes focus on the geometry and topology of Coxeter groups and buildings, especially nonspherical cases. The emphasis is on geometric intuition, and there are many examples and illustrations. Part I describes Coxeter groups and their geometric realisations, particularly the Davis complex, and Part II gives a concise introduction to buildings. This book will be suitable for mathematics graduate students and researchers in geometric group theory, as well as algebra and combinatorics. The assumed background is basic group theory, including group actions, and basic algebraic topology, together with some knowledge of Riemannian geometry.07aGroups & group theory2bicssc07aGroup theory and generalizations2msc40uhttps://doi.org/10.4171/189423cover imageuhttps://www.ems-ph.org/img/books/thomas_mini.jpg