May 2010 Mini Course (at Aalto University): Introduction to Lefschetz fixed point theorems
The course would be for 15 hours and is targeted at senior undergraduate students. The course assumes basic familiarity with Euclidian spaces and smooth functions on them and calculus in severable variables. It comprises of the following parts:
a) Introduction to differential topology. Basic concepts like manifolds, Saard’s theorem and de-Rham cohomology would be introduced in simple terms.
b) Transversality and orientation shall be described.
c) Basics of intersection theory shall be described and stability under homotopy explained.
d) The main statement and outline of proof of the classical Lefschetz fixed-point theorem is presented.