Math 132: Smooth Manifolds, Spring 2017

April 10

• Euler characteristic and the Poincaré-Hopf theorem.

March 3

• Transversality Preimage Theorem for Manifolds with Boundary - a proof of a Theorem from Section 2.1 in Guillemin-Pollack.
• An accompanying diagram for the above proof.

February 15

• The Diagnostic Quiz and solutions.

February 8

• Local Submersion Theorem - an outline of the proof of the Local Submersion Theorem.

February 5

• Prof. Taubes write some notes on the Inverse Function Theorem a few years ago, outlining a proof of the result. His proof is in the general setting of Banach spaces but it should be straightforward to see how to specialise the proof to open subsets of some Euclidean space.

February 3

• Local Immersion Theorem - an outline of the proof of the Local Immersion Theorem given in class. Please note that this version has a slight modification to the one handed out during class.
• Here is the giant diagram we are constructing in the proof of the Local Immersion Theorem. You should use this diagram as a visual aid when working through the proof. Note that the diagram is a slight modification of the one handed out in class.

January 23

• The Birth of Manifolds - a chapter from A Mathematical Gift III by Shiga & Sunada.