Mathematics

Dieter Balkenborg, Richard Bauer and Franz-Josef Bilitewski:

Beiträge zur Hierarchie der bimodularen Singularitäten

Diplomarbeit in der Mathematik

betreut von Egbert Brieskorn und Wolfgang Ebeling

Bonn 1984

On this page you find the scans of my Mathematics Diploma thesis co-written (in German) with Richard Bauer and Franz-Josef Bilitweski. I am currently using AI to transfer bits of the thesis into a latex file and then translate it into English. That is a very slow process and by the time it will be finished, AI can probably do it in a flash. Anyway, I constructed the latex file with the title page, the (very detailed) table of contents, a (first) translation of the introduction, two tables summarizing the main results, the bibliography and the details of who wrote which chapter. You can download that here in English and German.

AI says about the thesis:

"This diploma thesis was written in 1984 at the University of Bonn within the singularity theory group influenced by Egbert Brieskorn. It studies the classification and structure of so-called bimodal singularities in the sense of V. I. Arnold’s theory of singularities.

The main focus is on the hierarchy of these singularities, in particular their normal forms and the adjacency relations arising from deformations. The aim is to understand the position of bimodal singularities within Arnold’s classification by modality and to describe the transitions between different types.

The work forms part of the intensive research activity of the 1970s and 1980s devoted to the classification of isolated singularities, where the relationships between simple, unimodal and bimodal types were of central importance."

Modern mathematicians will be familiar with the following Mathematics Subject Classification

32Sxx — Singularities

32S05 — Local singularities
32S25 — Surface and hypersurface singularities
32S30 — Deformations of singularities
32S50 — Milnor fibration; topology of singularities

32S25 and 32S30 probably fit our thesis best, although all the above categories are relevant.