Generalized homology and cohomology theories
Student No.:40
Time:Mon&Wed, 15:20-16:55
Instructor:Thomas Farrell  [Tsinghua University]
Place:Conference Room 1, Jin Chun Yuan West Bldg.
Starting Date:2019-2-25
Ending Date:2019-5-17

Homology theory is characterized by the Eilenberg-Steenrod axioms found in their foundational 1952 book. One of these axioms is that the homology of a point is concentrated in degree 0 where it is the infinite cyclic group. If this axiom is deleted then several other interesting and useful extraordinary homology (and cohomology) theories arise: e.g. stable homotopy theory, cobordism theories, K-theory. G.W. Whitehead unified these general theories in his 1962 Transactions of the AMS paper. We will examine this general theory and the concrete examples mentioned above.

A basic graduate level course in algebraic topology.

1. P. Hilton, General Cohomology Theory and K-Theory
2. E. Spanier, Algebraic Topology
3. J.F. Adams, Infinite Loop Spaces