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Diff. Geometry III
   Summer 2014

 
TU LV-Nr:
3236 L 225
BMS Advanced Course:
Metric Comparison Geometry
Lectures:
Mon 8:30-10:00, 10:15-11:45, in room MA 848
Language:
This course will be held in English
Professor:
John M. Sullivan, MA 802, tel. 314-29279
sullivan@math.tu-berlin.de,
office hours Tuesday 11:30–12:30
Prerequisites:
Analysis, some geometry
WWW:
Course information is online at www3.math.tu-berlin.de/geometrie/Lehre/SS14/DGIII/
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
Note: the authors have posted corrections to the published version.
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 (Mon 14 Apr) will mainly review material on metric spaces. There is no lecture Easter Monday (21 Apr). The real work of the course will start Mon 28 Apr.

John Sullivan . 03.05.2014.
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