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Differential Geometry II (Winter 19)
– Analysis and geometry on manifolds –


Lecture 
Prof. John Sullivan 
Thu  14:0016:00  MA 841 
Thu  16:0018:00  MA 841 
Tutorial 
Chris Savva 
Tue  14:0016:00  MA 841 
Wed  10:0012:00  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 Covid19). 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 2024.1.2020 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 2024.1.2020 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) 14:0015:00.
 [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.

Name 
Office hours 
Room 
email @math.tuberlin.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 
MonFri 08:45–11:45  MA 801 
heintzel 
