Differential Geometry II Spring 2018

Prof. Dr. Dietmar A. Salamon
Charel Antony and Samuel Trautwein
Tue 8-10 ML H44, Thu 10-12 HG D 1.1


You will need to have a firm grip on the foundations of Differential Geometry and understand intrinsic manifolds. (See e.g. Chapter 2: Foundations of the lecture notes from Differential Geometry I .) Some exercises on the intrinsic setting will be provided in Exercise sheet 1.

Course Material

The first part of the course will follow the beautiful book Topology from the Differential Viewpoint by J. Milnor. The second part on intersection theory covers parts of the book Differential Topology by Guillemin and Pollock. The third part of the lecture on differential forms and DeRham cohomology will be covered by lecture notes which will be updated over the semester. If you spot any typos, please communicate these to the lecturer.

Short Description

Introduction to Differential Topology, including degree theory and intersection theory; Differential forms, including deRham cohomology and Poincare duality; Vector bundles, including Thom isomorphism and Euler number.

The new exercises will be posted here on Tuesday. We expect you to look at the problems before exercise class and to prepare questions for the exercise class on Friday.

If you want to hand in your solutions, please do so by the following Monday at 14:00 in your assistant's box in HG F28. Your solutions will usually be corrected and returned in the following exercise class or, if not collected, returned to the box in HG F28. Note that model solutions will be provided.

If you spot any mistakes or typos in the exercises or solutions, please communicate these to the coordinators.

exercise sheet due by solutions
Exercise sheet 1 February 26 Solutions 1
Exercise sheet 2 March 5 Solutions 2
Exercise sheet 3 March 12 Solutions 3
Exercise sheet 4 March 19 Solutions 4
Exercise sheet 5 March 26 Solutions 5
Exercise sheet 6 April 9 Solutions 6
Exercise sheet 7 April 16 Solutions 7
Exercise sheet 8 April 23 Solutions 8
Exercise sheet 9 April 30 Solutions 9
Exercise sheet 10 May 7 Solutions 10
Exercise sheet 11 May 14 Solutions 11
Exercise sheet 12 May 21 Solutions 12
Exercise sheet 13 May 28 Solutions 13
Exercise sheet 14
Fr 8-11HG E 1.1Charel & Samuel en

We will add books here that complement the material in class.