Real projective manifolds
Student No.:50
Time:Tue./Thu. 10:10-12:00
Instructor:Stephan Tillmann  [The University of Sydney]
Place:Conference Room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2012-7-3
Ending Date:2012-7-12

Course description:


This course begins with an introduction to real projective geometry (projective transformations; cross ratios; duality; projective manifolds;the special role of elliptic, euclidean and hyperbolic geometry). Key notions for the study of convex projective manifolds will then be described in detail (Hilbert metric;isometries; cusps;Busemann functions;horospheres; elementary groups;Margulis lemma). In the last lecture, an overview of what is known about strictly convex projective manifolds is given (thick-thin decomposition; topological finiteness; relative hyperbolicity).




Essential: Courses in Linear Algebra, Abstract Algebra and Metric Spaces.


Reference for the course:


(1) Yves Benoist: “A survey on divisible convex sets”,Geometry, analysis and topology of discrete groups, 1–18, Adv. Lect. Math. (ALM), 6, Int. Press, Somerville, MA, 2008.

(2) Herbert Busemann and Paul J. Kelly: “Projective geometry and Projective Metrics”, Academic Press Inc., New York, N. Y., 1953.

(3) Daryl Cooper, Darren Long, Stephan Tillmann: “On Convex Projective Manifolds and Cusps”, arXiv:1109.0585

(4) William P. Thurston: “Three-Dimensional Geometry and Topology”, Princeton University Press, Princeton, NJ, 1997.