Algebraic and Differential Topology
Syllabus:
1. Background on topology, manifolds, Lie groups, actions
2. Homotopy, fundamental group, covering spaces
3. Singular homology and cohomology
4. de Rham cohomology
5. Poincaré duality; Euler characteristic
6. Morse theory and applications
7. Fixed-point and degree theory; separation theorems
8. Fiber bundles, connections and Chern-Weil theory (time permitting)
Recommended Bibliography:
J. Rotman, An Introduction to Algebraic Topology, Springer Graduate Texts in Mathematics (1991)
J. Milnor, Morse Theory, Princeton University Press (1963)
R. Bott & L. Tu, Differential Forms in Algebraic Topology, Springer GTM 82, (1982)
I. Madsen & J. Tornehave, From Calculus to Cohomology, Cambridge U. P (1997)