Homotopy Theory and its relation to Differential Topology
Student No.:50
Time:Mon/Wed 13:00-14:50, 2015-03-09~ 2014-06-17(except for public holidays)
Instructor:Thomas Farrell  [Tsinghua University]
Place:Conference Room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2015-3-9
Ending Date:2015-6-17
The basics of homotopy theory through Hurewicz, Whitehead and Freudenthal suspension theorem will be covered, Followed by Serre’s generalization of these via his mod e homotopy related to the work of Pontryagin, Thom, Hirzebruch and Milnor.
Covering spaces, homology and cohomology through cup products and universal coefficient formula, Whitney embedding and Thom transversality theorems.
E.H. Spanier, Algebraic Topology
S-T Hu, Homotopy Theory
N. Steenrod, The Topology of Fibre Bundles
J. Milnor and J. Stasheff, Characteristic Classes