Cobordism Theory
Student No.:100
Time:16:30-17:30, 2016-6-3 (Fri.)
Instructor:John Francis  [Northwestern University]
Place:Lecture hall, Floor 3, Jin Chun Yuan West Building
Starting Date:2016-6-3
Ending Date:2016-6-3




Cobordism theory studies manifolds with boundary, where the boundary is not necessarily assumed to be connected. In particular, two compact n-manifolds M and N are said to be cobordant if there is a compact (n+1)-manifold with boundary W whose boundary is diffeomorphic to the disjoint union of M and N. I will give a historically-minded overview of aspects of cobordism theory. This overview will draw from Pontryagin and Thom's original works, the relation of homotopy groups of spheres and framed cobordism; Hirzebruch's signature theorem and Milnor's discovery of exotic spheres; surgery, Morse theory, and the classification of manifolds; cobordism categories and the entry, after Segal and Atiyah, into physics; and the Baez–Dolan cobordism hypothesis, classifying functors from cobordism categories.