Course Syllabus

The official course plan is here.

Main topics:

• smooth manifolds and smooth maps
• tangent bundles, immersions, submersions, embeddings
• Sard's theorem, immersions and embeddings of manifolds into Euclidean space
• Transversality
• Intersection theory, mod-2 and integrally
• Applications (Jordan-Brouwer theorem, Borsuk-Ulam theorem)
• Lefschetz fixed point theorem, Euler characteristic, Hopf degree theorem
• Either: Introduction to Morse theory
• Or: The topology of Lie groups

A more detailed plan will appear at a later stage.