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Strasbourg Master Class on Geometry
IRMA Lectures in Mathematics and Theoretical Physics Vol. 18

Strasbourg Master Class on Geometry

Editor:
Athanase Papadopoulos (IRMA, Strasbourg, France)


ISBN print 978-3-03719-105-7, ISBN online 978-3-03719-605-2
DOI 10.4171/105
January 2012, 461 pages, softcover, 17.0 x 24.0 cm.
48.00 Euro

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 to fifth-year students and PhD students in mathematics the opportunity to learn new topics that lead directly to the current research in geometry and topology. The courses were held 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, Teichmüller theory, Lie groups and asymptotic geometry.

The text is addressed to students and mathematicians who wish to learn the subject. It can also be used as a reference book and as a textbook for short courses on geometry.

Keywords: Hyperbolic geometry, hyperbolic space, neutral geometry, Euclid’s axioms, hyperbolic trigonometry, spherical geometry, Khayyam–Saccheri quadrilaterals, trirectangular quadrilaterals, parallelism, horocycle, Lobachevsky parallelism function, Beltrami–Klein

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