MATH 7530: Algebraic Topology II (Fall 2011)

Instructor: Allen Hatcher

This is a second-semester course in Algebraic Topology, the continuation of MATH 6510. The material will mostly be chosen from the second half of my algebraic topology textbook. Some likely topics:

Chapter 3: Cohomology

• universal coefficient theorems
• cup products
• the Künneth formula
• Poincaré duality
• H-spaces and Hopf algebras,

Chapter 4: Homotopy Theory

• homotopy groups
• Whitehead's theorem
• cellular approximation of maps
• CW approximations to spaces
• the Hurewicz theorem
• the Freudenthal suspension theorem
• fiber bundles and fibrations
• the Hopf invariant
• Eilenberg-MacLane spaces

Further topics as time permits.