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Differential Geometry II (Winter 19)
– Analysis and geometry on manifolds –
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Lecture |
Prof. John Sullivan |
Thu | 14:00-16:00 | MA 841 |
Thu | 16:00-18:00 | MA 841 |
Tutorial |
Chris Savva |
Tue | 14:00-16:00 | MA 841 |
Wed | 10:00-12:00 | MA 376 |
This course is a BMS basic course and the lectures will be in English. Please feel free to ask any questions during lectures in English or German. Homework should be submitted in English.
News
- [2020, Oct 12]
- Exams will also be offered 27–30 October.
- [2020, Sep 9]
- Exams will be offered 28–30 September and 7–8 October.
- [2020, Mar 17]
- The mathematics deparment has instructed us to cancel all planned
exams until at least 20 April (because of Covid-19). There will be no exams
the first week of April. I will offer exams again after the start
of the semester.
- [2020, Feb 27]
- Lecture notes including the final lectures have now been posted.
- [2020, Feb 27]
- Exams
will be offered on the following days:
1, 2 and 3 April.
- [2020, Feb 3]
- Exams
will be offered on the following days:
13, 14, 24 and 26 February, as well as in the week of 30 March – 3 April.
- [2020, Feb 3]
- There will be no lecture on 13 February.
- [2020, Jan 30]
- Exercise Sheet 13 is now posted. This is the last Exercise Sheet.
- [2020, Jan 14]
- The week of 20-24.1.2020 there will be a tutorial only on Wednesday 22.1.2020. The tutorial of Tuesday 21.1.2020 is cancelled. Office hours for Chris for the week of 20-24.1.2020 will be by appointment.
- [2020, Jan 14]
- Office hours for Chris on Wednesday (15.1.2020) are cancelled.
- [2020, Jan 6]
- This week (9.1.2020) there will only one lecture 14:15–15:45.
- [2019, Nov 19]
- Office hours for Chris on Wednesday (20.11.2019) are cancelled. Instead, there will be office hours on Friday (22.11.2019) 14:00-15:00.
- [2019, Nov 15]
- Exercise Sheet 5 is now posted. Make sure to check the current version since there was a mistake when initially posted.
- [2019, Oct]
- Exersise Sheet 3 is now posted. Updated office hours for Chris.
- [2019, Oct]
- Exersise Sheet 2 is now posted. On the Exercise Sheet 1, Exercise 3 is updated as already discussed.
- [2019, Oct]
- The first lecture is on Thursday, October 17. Tutorials start the second week on October 22 and 23.
Contents
Differentiable manifolds, vector bundles, differential forms, Riemannian geometry.
Lecture Notes
Updated lecture notes as of
27 February.
Please email Prof. Sullivan with any suggestions
for corrections or improvements!
For comparison, here
is the version from Winter 2015/16.
Note that the course Differential Geometry I (Curves and Surfaces) is
not strictly a prerequisite for this course. It gives useful geometric
insight on the lower dimensional cases but is logically independent:
the courses can be taken in either order. For reference, here are Prof. Sullivan's
lecture notes from last semester.
Homework
- Exercise sheet 13, due before the lecture on February 6, 2020.
- Exercise sheet 12, due before the lecture on January 30, 2020.
- Exercise sheet 11, due before the lecture on January 23, 2020.
- Exercise sheet 10, due before the lecture on January 16, 2020.
- Exercise sheet 9, due before the lecture on December 19, 2019.
- Exercise sheet 8, due before the lecture on December 12, 2019.
- Exercise sheet 7, due before the lecture on December 5, 2019.
- Exercise sheet 6, due before the lecture on November 28, 2019.
- Exercise sheet 5, due before the lecture on November 21, 2019.
- Exercise sheet 4, due before the lecture on November 14, 2019.
- Exercise sheet 3, due before the lecture on November 7, 2019.
- Exercise sheet 2, due before the lecture on October 31, 2019.
- Exercise sheet 1, due before the lecture on October 24, 2019.
Literature
- Kühnel, Differential Geometry / Differentialgeometrie, AMS / Vieweg
- Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, 2nd Ed, Academic Press
- Bröcker and Jänich, Introduction to Differential Topology / Einführung in die Differentialtopologie, CUP / Springer
- Warner, Foundations of Differentiable Manifolds and Lie Groups, GTM 94, Springer
- Morgan, Riemannian Geometry: A Beginner's Guide, 2nd Ed, A K Peters
- Bishop and Goldberg, Tensor Analysis on Manifolds, Dover
- Milnor, Topology from the Differentiable Viewpoint, U P Virginia
- Spivak, Calculus on Manifolds, Benjamin/Cummings
- Sharpe, Differential Geometry, GTM 166, Springer
Homework policy
- Homework should be turned in by groups of two students (in English).
- Homework is due weekly at the beginning of the lecture on Thursday.
- To get a certificate for the tutorial and qualify to take the oral exam at the end of the semester, you need to get at least 60% of the points on the homework assignments.
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Name |
Office hours |
Room |
email @math.tu-berlin.de |
Lecturer |
Prof. John Sullivan |
TBA | MA 802 |
sullivan |
Assistant |
Chris Savva |
Tue 16:00–17:00, Wed 12:00–13:00 | MA 804 |
savva |
Secretary |
Heather Heintzel |
Mon-Fri 08:45–11:45 | MA 801 |
heintzel |
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