List of Potential Topics:

• Proof of Sard's Theorem
• Proof of Morse Lemma
• Elements of Morse Theory
• Poincare-Hopf Theorem (if not covered in class)
• Lefschetz Fixed Point Theory (if not covered in class)
• Hopf Degree Theorem
• Any part of Chapter 4 (Integration on Manifolds)
• Stiefel-Whitney classes
• Elements of Cobordism Theory
• Classification of 1-manifolds
• . . .