| Instructor | Prof. John Loftin, 323 Smith, Phone: 5156 ext. 23. |
| loftin@ andromeda. rutgers. edu | |
| Website | www.andromeda.rutgers.edu/~loftin (this syllabus is attached to the website) |
| Text | Differential Topology, by Guillemin and Pollack |
| Supplemental reading | Calculus on Manifolds, by Spivak
Differential Topology, by Hirsch |
| Prerequisites | Linear algebra; advanced calculus (the chain rule, differentiable maps between Euclidean spaces) |
| Topics | Manifolds, Inverse Function Theorem, Immersions, Submersions, Transversality, Whitney's Theorem, Homotopy, Intersection Theory, Applications |
| Homework | Homework will be collected about every 2 weeks. |
Tentative outline of topics:
1. Manifolds and Smooth Maps
a. Chapter 1 of Guillemin and Pollack
b. The Inverse Function Theorem (Spivak)
c. The real definition of smooth manifold,
Whitney's Theorem (Hirsch)
d. Topics in general topology (as needed)
2. Transversality and Intersection (Chapter 2 of Guillemin and
Pollack)
3. Oriented Intersection Theory (Chapter 3 of Guillemin and Pollack)