000			03802nam a22003738i 4500
001			CR9780511549656
003			UkCbUP
005			20200124160240.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090511s2001||||enk o ||1 0|eng|d
020			_a9780511549656 (ebook)
020			_z9780521660587 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA471 _b.P73 2001
082	0	0	_a516/.5 _221
100	1		_aPolster, Burkard, _eauthor.
245	1	0	_aGeometries on surfaces / _cBurkard Polster and Günter Steinke.
264		1	_aCambridge : _bCambridge University Press, _c2001.
300			_a1 online resource (xxii, 490 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aEncyclopedia of mathematics and its applications ; _vvolume 84
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0	0	_tGeometries for Pedestrians -- _tGeometries of Points and Lines -- _tGeometries on Surfaces -- _tFlat Linear Spaces -- _tModels of the Classical Flat Projective Plane -- _tConvexity Theory -- _tContinuity of Geometric Operations and the Line Space -- _tIsomorphisms, Automorphism Groups, and Polarities -- _tTopological Planes and Flat Linear Spaces -- _tClassification with Respect to the Group Dimension -- _tConstructions -- _tPlanes with Special Properties -- _tOther Invariants and Characterizations -- _tRelated Geometries -- _tSpherical Circle Planes -- _tModels of the Classical Flat Mobius Plane -- _tDerived Planes and Topological Properties -- _tConstructions -- _tGroups of Automorphisms and Groups of Projectivities -- _tThe Hering Types -- _tCharacterizations of the Classical Plane -- _tPlanes with Special Properties -- _tSubgeometries and Lie Geometries -- _tToroidal Circle Planes -- _tModels of the Classical Flat Minkowski Plane -- _tDerived Planes and Topological Properties -- _tConstructions -- _tAutomorphism Groups and Groups of Projectivities -- _tThe Klein-Kroll Types -- _tCharacterizations of the Classical Plane -- _tPlanes with Special Properties -- _tSubgeometries and Lie Geometries -- _tCylindrical Circle Planes -- _tModels of the Classical Flat Laguerre Plane -- _tDerived Planes and Topological Properties -- _tConstructions -- _tAutomorphism Groups and Groups of Projectivities -- _tThe Kleinewillinghofer Types -- _tCharacterizations of the Classical Plane -- _tPlanes with Special Properties -- _tSubgeometries and Lie Geometries -- _tGeneralized Quadrangles.
520			_aThe projective, Möbius, Laguerre, and Minkowski planes over the real numbers are just a few examples of a host of fundamental classical topological geometries on surfaces. This book summarizes all known major results and open problems related to these classical point-line geometries and their close (nonclassical) relatives. Topics covered include: classical geometries; methods for constructing nonclassical geometries; classifications and characterizations of geometries. This work is related to many other fields including interpolation theory, convexity, the theory of pseudoline arrangements, topology, the theory of Lie groups, and many more. The authors detail these connections, some of which are well-known, but many much less so. Acting both as a reference for experts and as an accessible introduction for graduate students, this book will interest anyone wishing to know more about point-line geometries and the way they interact.
650		0	_aGeometry, Projective.
650		0	_aSurfaces.
700	1		_aSteinke, Günter, _d1955- _eauthor.
776	0	8	_iPrint version: _z9780521660587
830		0	_aEncyclopedia of mathematics and its applications ; _vv. 84.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511549656
999			_c518422 _d518420