Course Code : | 2600WETAND |

Study domain: | Mathematics |

Academic year: | 2019-2020 |

Semester: | 1st semester |

Contact hours: | 30 |

Credits: | 3 |

Study load (hours): | 84 |

Contract restrictions: | No contract restriction |

Language of instruction: | English |

Exam period: | exam in the 1st semester |

Lecturer(s) | Joseph Palmer |

At the start of this course the student should have acquired the following competences:

an active knowledge of

an active knowledge of

- English

- English

Some basic knowledge of differential geometry, general/algebraic topology, and multivariable calculus should be sufficient.

- Knowledge and experience with Morse theory and Morse functions
- Knowledge and experience with Morse homology

We will cover the first three chapters of "Morse theory and Floer homology" by Michèle Audin and Mihai Damian, and possibly some parts of the forth chapter. This means we will cover most of "Part I: Morse Theory" but we will not cover any part of the second part of the book, concerning Floer homology.

This includes:

1. Introduction to Morse functions

2. The Morse lemma

3. Pseudo-gradients

4. Definting the Morse complex

5. Applications of the Morse complex (Poincare duality, Euler characteristic, etc)

Class contact teachingLectures

Personal workExercises Assignments Individually

Personal work

ExaminationOral without written preparation

Continuous assessmentAssignments

Continuous assessment

We will be following the textbook "Morse theory and Floer homology" by Michèle Audin and Mihai Damian. We will cover Part I of the text, which is comprised of chapters 1-4.

link: https://www.amazon.com/Morse-Theory-Floer-Homology-Universitext/dp/1447154959

ISBN-10: 1447154959

ISBN-13: 978-1447154952

The lecture notes will also be posted on blackboard throughout the course.

Joseph.Palmer@uantwerpen.be