02544nam 22005175 450 991033824760332120210708142118.03-030-05312-110.1007/978-3-030-05312-3(CKB)4100000008153870(MiAaPQ)EBC5771143(DE-He213)978-3-030-05312-3(PPN)236523511(EXLCZ)99410000000815387020190508d2019 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierAn Invitation to Alexandrov Geometry CAT(0) Spaces /by Stephanie Alexander, Vitali Kapovitch, Anton Petrunin1st ed. 2019.Cham :Springer International Publishing :Imprint: Springer,2019.1 online resource (95 pages)SpringerBriefs in Mathematics,2191-81983-030-05311-3 1 Preliminaries -- 2 Gluing theorem and billiards -- 3 Globalization and asphericity -- 4 Subsets -- 5 Semisolutions.Aimed toward graduate students and research mathematicians, with minimal prerequisites this book provides a fresh take on Alexandrov geometry and explains the importance of CAT(0) geometry in geometric group theory. Beginning with an overview of fundamentals, definitions, and conventions, this book quickly moves forward to discuss the Reshetnyak gluing theorem and applies it to the billiards problems. The Hadamard–Cartan globalization theorem is explored and applied to construct exotic aspherical manifolds.SpringerBriefs in Mathematics,2191-8198Differential geometryGroup theoryDifferential Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21022Group Theory and Generalizationshttps://scigraph.springernature.com/ontologies/product-market-codes/M11078Differential geometry.Group theory.Differential Geometry.Group Theory and Generalizations.513.8516.373Alexander Stephanieauthttp://id.loc.gov/vocabulary/relators/aut780987Kapovitch Vitaliauthttp://id.loc.gov/vocabulary/relators/autPetrunin Antonauthttp://id.loc.gov/vocabulary/relators/autBOOK9910338247603321An Invitation to Alexandrov Geometry2510889UNINA