Departement Mathematik und Statistik

Herbst 2016

Seminar: Morse and Floer Homology (HS 2016)

Lecturer

  • Prof. Dr. Sebastian Baader

Date and Venue

  • Monday, 14 - 16 h, B13 (ExWi)
  • Start: Monday, September 19, 2016

Details

  • 3 ECTS credit points

Description

In this seminar we aim to understand Morse homology, an important invariant of differentiable manifolds. The construction of this invariant is based on the structure of flow lines of so-called Morse functions. We intend to start with elementary Morse theory and will provide the necessary background in homology. As an application, we will obtain the Morse inequalities. Depending on progress, we will study a powerful generalization called Floer homology, which has spectacular applications in symplectic geometry.

Basic knowledge of topology and differential geometry is useful; Draisma's lecture on algebraic topology is an excellent complement.

Literature:

  1. Audin and Damian: Morse Theory and Floer Homology
  2. Michael Hutchings: Lecture Notes on Morse Homology (available online)
  3. John Milnor: Morse Theory