Diff Geo III
SS 2011

 
TU LV-Nr:
3236 L 225
BMS Advanced Course:
Metric Comparison Geometry
Lectures:
Mon,Thu 10-12, in room MA 313
Language:
This course will be held in English
Professor:
John M. Sullivan, MA 318, tel. 314-29279
sullivan@math.tu-berlin.de,
office hours TBA or by appointment
Prerequisites:
Analysis, some geometry
News:
The lecture on Thursday 28 April will be slightly later than usual: roughly 10:50 – 12:10.
WWW:
Course information is online at www.math.tu-berlin.de/~sullivan/L/11S/DG3/
Course work:
homework (not to be turned in), oral final exam
Reccomended homework:
  • 1.2.10, 1.4.{5,10}, 1.5.4
  • 2.1.3, 2.3.{2,3,7,8,9,10,11}
  • 2.4.{5,18,19}, 2.5.{3,6,18}
Textbook:
Burago, Burago, Ivanov: A Course in Metric Geometry, AMS Grad. Stud. in Math. 33
Other books:
Gromov: Metric structures for Riemannian and non-Riemannian spaces, Birkhäuser, 2007
Ballmann: Lectures on spaces of nonpositive curvature, Birkhäuser, 1995
Buyalo, Schroeder: Spaces of curvature bounded above, Int'l Press, 2007
Brisdon, Haefliger: Metric spaces of non-positive curvature, Springer GdMW 319, 1999
Outline:
This course will cover the geometry of length spaces (also called geodesic metric spaces), in particular those with curvature bounded above or below by some constant. This relatively new field, initiated by Alexandrov among others, extends results from Riemannian geometry to nonsmooth spaces, in a sense unifying smooth and polyhedral geometry.
Note:
The first lecture on Monday 11 April reviewed material on metric spaces. There is no lecture on Thursday 14 April. The real work of the course will start on Monday 18 April.