|Low dimensional manifolds|
|Time：||10:10-12:00 every Tue and Thu from Feb. 21-Mar. 29|
|Instructor：||Hyam Rubinstein [University of Melbourne]|
|Place：||Conference Room 1, Floor 1, Jin Chun Yuan West Building|
The combinatorial geometry and topology of 3-manifolds and aspherical 4-manifolds will be developed. With a fixed triangulation, hypersurfaces can be represented in normal or almost normal form. The theory of sweepouts will be described, which is a form of Morse theory for hypersurfaces.
Haken n-manifolds will be explored and it will be shown that they are abundant in dimension 4. Haken cobordism itheory n dimension 4 will be computed.
Beginning courses in algebraic topology, differential topology, differential geometry would be very helpful.
Reference for the course:
Jaco, Lectures on 3-manifold topology, American Math Soc
Hempel, 3-manifolds, Princeton University Press
Jaco-Rubinstein, 0-efficient triangulations of 3-manifolds, J. of Diff Geom, 65 (2003), 61-168.