Strasbourg Master Class on GeometryAthanase Papadopoulos European Mathematical Society, 2012 - 454 σελίδες This book contains carefully revised and expanded versions of eight courses that were presented at the University of Strasbourg during two geometry master classes in 2008 and 2009. The aim of the master classes was to give fifth-year students and Ph.D. students in mathematics the opportunity to learn new topics that lead directly to the current research in geometry and topology. The courses were taught by leading experts. The subjects treated include hyperbolic geometry, three-manifold topology, representation theory of fundamental groups of surfaces and of three-manifolds, dynamics on the hyperbolic plane with applications to number theory, Riemann surfaces, Teichmuller theory, Lie groups, and asymptotic geometry. The text is aimed at graduate students and research mathematicians. It can also be used as a reference book and as a textbook for short courses on geometry. |
Περιεχόμενα
Hyperbolic spaces | 3 |
Norbert ACampo and Athanase Papadopoulos | 4 |
Area | 5 |
rue René Descartes 67084 Strasbourg Cedex France | 7 |
Quasimetric spaces and their Möbius geometry | 10 |
9 | 31 |
4 | 55 |
6 | 80 |
Models | 139 |
Françoise Dal | 183 |
Frank Herrlich | 233 |
Introduction | 245 |
Philipp Korablev and Sergey Matveev | 255 |
Gabriele Link | 285 |
Julien Marché | 333 |
Carlo Petronio | 371 |
Συχνά εμφανιζόμενοι όροι και φράσεις
3-manifold angle of parallelism angle sum angular deficit automorphism axioms boundary centered circle congruent consider contains Corollary cosh curves decomposition defined definition denote disjoint disk distance edge element elliptic equal equation equidistant equivalent Euclid's Euclid's Elements Euclidean geometry Euclidean plane exists fact Figure finite function geodesic given H₁ homeomorphism horocycle hyperbolic geometry hyperbolic plane hypercycle integer intersection isometries isomorphic Khayyam-Saccheri quadrilateral l₁ Lemma length Lobachevsky manifold Math metric neutral geometry neutral plane Note notion obtain origami orthogonal parallel postulate perpendicular bisector polygon projection Proof properties Proposition prove quadratic form real numbers respectively Riemannian Riemannian metric right angles right triangle Saccheri's satisfying Section segment sequence sinh sphere spherical geometry subgroup surface symmetric space T¹H T¹S tanh tetrahedra Theorem topology trajectory transformation translation trigonometric formulae trirectangular quadrilateral vector vertex vertices