## Differential Geometry

### Guide to Stokes’ Theorem

In the winter term 1970/71 Günter Harder was lecturing on differential geometry for students of the 3rd semester (Infinitesimalrechnung 3) at University of Bonn. I was mentoring one of the groups doing the exercises. As the class started to become tough for the group I offered to run a workshop at the end of the term during the vacation. The material was determined by the students and I wrote it up during the next term. The draft was then given to the university printing office and photocopied and distributed in October 1971.

This is an English translation (and typeset in AMS-LaTeX) of the otherwise unchanged notes.

### My degree dissertation: On differential forms in the Thom class

- version 1.1, 2011-04-30 :

first published: 2002-04-22

MSC Primary 55N33, Secondary 53C05, 55R25, 57R25, 58A12, 58A14

This paper is an English translation of my degree dissertation (Diplomarbeit), prepared with AMS-LaTeX. The original title was *Über explizite Formeln für Differentialformen aus der Thomklasse*.

It contains a construction of differential forms on vector bundles that represent the *Thom* cohomology class. These forms can be used to calculate intersection numbers. A proof of the Gauss-Bonnet formula is given as application.

I submitted the degree dissertation on 31 October 1972 to the Mathematics and Science Faculty of the University of Bonn, and was granted the diploma on 21 November 1972 by the dean Rolf Leis. Referees for the dissertation have been Günter Harder and Jacques Tits, other members of the board of examiners have been Pierre Gabriel (in Pure Mathematics and Representation Theory), Rolf Leis (in Applied Mathematics) and Wolfgang Priester (in Astronomy).