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000890281 019__ $$a1105186392
000890281 020__ $$a9783030053123$$q(electronic book)
000890281 020__ $$a3030053121$$q(electronic book)
000890281 020__ $$z9783030053116
000890281 0247_ $$a10.1007/978-3-030-05
000890281 035__ $$aSP(OCoLC)on1100588432
000890281 035__ $$aSP(OCoLC)1100588432$$z(OCoLC)1105186392
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000890281 049__ $$aISEA
000890281 050_4 $$aQA641
000890281 08204 $$a516.373$$223
000890281 1001_ $$aAlexander, Stephanie,$$eauthor.
000890281 24513 $$aAn invitation to Alexandrov geometry :$$bCAT(0) spaces /$$cStephanie Alexander, Vitali Kapovitch, Anton Petrunin.
000890281 264_1 $$aCham, Switzerland :$$bSpringer,$$c[2019]
000890281 300__ $$a1 online resource.
000890281 336__ $$atext$$btxt$$2rdacontent
000890281 337__ $$acomputer$$bc$$2rdamedia
000890281 338__ $$aonline resource$$bcr$$2rdacarrier
000890281 4901_ $$aSpringerBriefs in mathematics,$$x2191-8201
000890281 504__ $$aIncludes bibliographical references and index.
000890281 5050_ $$aIntro; Preface; Early history of Alexandov geometry; Manifesto of Alexandrov geometry; Acknowledgements; Contents; 1 Preliminaries; 1.1 Metric spaces; 1.2 Constructions; 1.3 Geodesics, triangles, and hinges; 1.4 Length spaces; 1.5 Model angles and triangles; 1.6 Angles and the first variation; 1.7 Space of directions and tangent space; 1.8 Hausdorff convergence; 1.9 Gromov-Hausdorff convergence; 2 Gluing theorem and billiards; 2.1 The 4-point condition; 2.2 Thin triangles; 2.3 Reshetnyak's gluing theorem; 2.4 Reshetnyak puff pastry; 2.5 Wide corners; 2.6 Billiards; 2.7 Comments
000890281 5058_ $$a3 Globalization and asphericity3.1 Locally CAT spaces; 3.2 Space of local geodesic paths; 3.3 Globalization; 3.4 Polyhedral spaces; 3.5 Flag complexes; 3.6 Cubical complexes; 3.7 Exotic aspherical manifolds; 3.8 Comments; 4 Subsets; 4.1 Motivating examples; 4.2 Two-convexity; 4.3 Sets with smooth boundary; 4.4 Open plane sets; 4.5 Shefel's theorem; 4.6 Polyhedral case; 4.7 Two-convex hulls; 4.8 Proof of Shefel's theorem; 4.9 Comments; Semisolutions; References; ; Index
000890281 506__ $$aAccess limited to authorized users.
000890281 520__ $$aAimed toward graduate students and research mathematicians, with minimal prerequisites this book provides a fresh take on Alexandrov geometry and explains the importance of CAT(0) geometry in geometric group theory. Beginning with an overview of fundamentals, definitions, and conventions, this book quickly moves forward to discuss the Reshetnyak gluing theorem and applies it to the billiards problems. The Hadamard–Cartan globalization theorem is explored and applied to construct exotic aspherical manifolds.
000890281 588__ $$aOnline resource; title from PDF title page (viewed May 10, 2019).
000890281 650_0 $$aGeneralized spaces.
000890281 650_0 $$aRiemannian manifolds.
000890281 650_0 $$aGeometry, Riemannian.
000890281 7001_ $$aKapovitch, Vitali,$$eauthor.
000890281 7001_ $$aPetrunin, Anton,$$eauthor.
000890281 830_0 $$aSpringerBriefs in mathematics.
000890281 852__ $$bebk
000890281 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-030-05312-3$$zOnline Access$$91397441.1
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000890281 980__ $$aEBOOK
000890281 980__ $$aBIB
000890281 982__ $$aEbook
000890281 983__ $$aOnline
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