Morse Theory
Welcome to the course on "Morse Theory". The theory tries to understand the topology of differentiable manifolds with the help of the theory of dynamical systems, in particular the gradient system corresponding to a smooth (in fact a Morse) function on the manifold. It is an important theory within the realm of Differential Geometry and Algebraic Topology.
Prerequisites: Besides a good knowledge of the fundamental courses on Linear Algebra and Analysis some knowledge about differentiable manifolds as well as dynamical systems would be helpful.
Examination: The final examination of the course will be done by a homework about a topic of the course. Usually you get 4-6 weeks for a text about 5 or 6 pages after the end of the last lecture.
Literature: (1) Hirsch, Morris W.: Differential Topology. Springer-Verlag. (2) Milnor, J.: Morse Theory. Princeton University Press. (3) Hirsch, M.W., Smale, S.: Differential equations, dynamical systems, and linear algebra. Academic Press.
Start: The first lecture will be at October, 21st., 8-10 in lecture room N14 in the C-building.
Language: The course will be held in english language.
Registration: If you are interested in participating the course you may register on the platform ILIAS under the link
https://ovidius.uni-tuebingen.de/ilias3/goto.php?target=crs_3888557_rcodehDtaLR3YUQ&client_id=pr02
The password is: "Milnor".
In the sequel I will write actual informations due to the course in form of a blog here:
(8) 27.01.2023: Let me terminate the deadline for your homework on
Friday, March 31st.
I will try to read your work immediately after that so that we can finish the course before the beginning of the lecture time in the summer semester.
(7) 23.12.2022: Today there was again a little bit a mess with the numeration in the notes of the lecture (Lecture-09). The last page (unnumbered, after page 17) must be filled in as page 14,5 so-to-say between pages 14 and 15. It contains the end of a proof. I apologize for this. Again I want to wish you a Merry Christmas and a Happy New Year. I hope we will see again on Friday, January, 13th, for Lecture-10.
(6) 16.12.2022: Here is the zoom-Link for the lecture next week on December 23 th. The lecture takes place at lecture hall N 14, as usual, but I try to share what I'll write on the tablet in the zoom conference room. Note that there will be not an asynchron offer (no record of the lecture). I hope to see you. Otherwise I wish you all Merry Christmas and a Happy New Year.
Zoom-Link: https://zoom.us/j/98434539
(5) 09.12.2022: Please remember the decision from the head of the university that in the last week before christmas all lectures will be only online since the buildings of the university will be cold (for saving energy costs). So on Friday 12/23, the lecture will be via a conference room of the platform "zoom". I will give you here the link for it next week. Nevertheless I will be then at our usual lecture room N 14 and give the lecture from there using the tablet which I have only there. So, if you want, you could also come to N 14, also on this Friday, but take a cover or a warm coat with you.
(4) 15.11.2022: Due to another duty at this day the lecture on 12/02 must unfortunately be cancelled. I apologize for this. Next lecture will be on December, 9 th.
(3) 11.11.2022: With the numbering of the pages in the notes for the lecture from today there has been something wrong. One page has no number at all and the last page must be filled inside between the pages 15 and 16. Sorry for that.
(2) 28.10.2022: Today I had problems in connecting the computer with the tablet in lecture room N14. Therefore I wrote my notes for the lecture on the board. But I copied my notes and put them into an pdf file which you can find in the navigation column on the right if you was not in the lecture this morning. Next week I think I will use the tablet again.
(1) The notes from the lecture are now also available on the navigation column on the right.