Course details
Semester
- Autumn 2023
- Monday, October 2nd to Friday, December 8th
Hours
- Live lecture hours
- 10
- Recorded lecture hours
- 0
- Total advised study hours
- 40
Timetable
- Mondays
- 10:05 - 10:55 (UK)
Description
This theory studies the topology of smooth manifolds through real-valued smooth functions whose critical points satisfy a certain non-degeneracy condition.
We will investigate how the homotopy type is related to critical points and how the homology of a manifold can be calculated through Morse functions.
Prerequisites
This can be obtained through the Core Courses MAGIC063 and MAGIC064.
Syllabus
- Smooth functions, non-degenerate critical points, Morse functions.
- Morse Lemma.
- Morse functions on spheres, projective spaces, orthogonal groups, configuration spaces of linkages.
- Homotopy type, cell decompositions of manifolds.
- Existence of Morse functions, cobordisms.
- Gradient flows, stable and unstable manifolds.
- Resonant Morse functions, ordered Morse functions.
- Morse homology, Morse inequalities.
- Calculations for projective spaces.
- Introduction to the h-cobordism theorem.
Lecturer
-
DS
Dr Dirk Schuetz
- University
- Durham University
Bibliography
No bibliography has been specified for this course.
Assessment
The assessment for this course will be released on Monday 8th January 2024 at 00:00 and is due in before Friday 19th January 2024 at 11:00.
Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).
You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).
If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.
Please note that you are not registered for assessment on this course.
Files
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Lectures
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