19 036: COMPUTATIONAL TOPOLOGY

Term: Summer 2008
Time: Tue Wed 10:00 - 12:00
Location: Arnimallee 3, SR 005
Instructors: Herbert Edelsbrunner

announcements schedule references

Announcements

Schedule

Date Lecture Topic Notes Assignments
Apr 15 Tue introduction
General information [pdf]  
  I. GRAPHS    
Apr 16 Wed connected components
Lecture [pdf]  
Apr 22 Tue curves
Lecture [pdf] [pdf]  
Apr 23 Wed planar graphs
Lecture [pdf] HW#1 out [pdf]
  II. SURFACES    
Apr 29 Tue two-dimensional manifolds
Lecture [pdf] [pdf] [pdf]  
Apr 30 Wed surface simplification
Lecture [pdf] HW#2 out [pdf]
  III. COMPLEXES    
May 06 Tue simplicial complexes
Lecture [pdf]  
May 07 Wed convex set systems
Lecture [pdf]  
May 13 Tue Delaunay complexes
Lecture [pdf]  
May 14 Wed alpha complexes
Lecture [pdf] HW#3 out [pdf]
  IV. HOMOLOGY    
May 20 Tue homology groups
Lecture  
May 21 Wed matrix reduction
Lecture  
May 27 Tue exact sequences
Lecture  
May 28 Wed Mayer-Vietoris
Lecture HW#4 out
  V. DUALITY    
Jun 03 Tue cohomology
Lecture  
Jun 04 Wed Poincare duality
Lecture  
Jun 10 Tue intersection theory
Lecture HW#5 out
  VI. MORSE FUNCTIONS    
Jun 11 Wed generic smooth functions
Lecture  
Jun 17 Tue piecewise linear functions
Lecture  
Jun 18 Wed Reeb graphs
Lecture HW#6 due
  VII. PERSISTENCE    
Jun 24 Tue persistent homology
Lecture  
Jun 25 Wed stability
Lecture  
Jul 01 Tue an application to curves
Lecture HW#7 due

References

[1] P. S. Alexandroff. Elementary Concepts in Topology. translated by A. E. Farley, Dover, New York, 1961.
[2] H. Edelsbrunner. Geometry and Topology for Mesh Generation. Cambridge Univ. Press, England, 2001.
[3] P. J. Giblin. Graphs, Surfaces and Homology. 2nd edition, Chapman and Hall, London, 1977.
[4] Y. Matsumoto. An Introduction to Morse Theory. Amer. Math. Soc., Providence, Rhode Island, 2002.
[5] J. W. Milnor. Topology from the Differential Viewpoint. Princeton Univ. Press, New Jersey, 1965.
[6] J. R. Munkres. Topology. A First Course. Prentice-Hall, Englewood Cliffs, New Jersey, 1975.
[7] J. R. Munkres. Elements of Algebraic Topology. Perseus, Cambridge, Massachusetts, 1984.
[8] R. E. Tarjan. Data Structures and Network Algorithms. SIAM, Philadelphia, Pennsylvania, 1983.

announcements schedule references

Herbert Edelsbrunner (edels@cs.duke.edu) April 2008