Ist 4 denn noch normal?

Abstract

This song in the style of a moritat was composed by Wulf-Dieter Geyer for the Geyer-Harder Arbeitsgemeinschaft in Oberwolfach in the fall of 1984. The Arbeitsgemeinschaft is one of the most attractive activities at Mathematisches Forschungsinstitut Oberwolfach (see the article by J. Neukirch in this book). It meets twice a year and brings together mathematicians from different areas to learn a recent particularly interesting development in mathematics. At the end of each such meeting the participants decide in a long democratic procedure (with a complicated system of voting, only very experienced people like Geyer and Harder can conduct) what should be the topic of the next meeting. Besides being of general interest the topic has to be accessible to a wider range of mathematicians. The participants of the spring meeting 1984 decided that it would be time to learn the fascinating new results on 4-manifolds. But would it be accessible to normal mathematicians? My personal opinion at this time was that the delicate shrinking arguments of Freedman’s proof were almost unaccessible (my standard phrase was: “Only accessible to those selected by god”). But, his statements were easily understandable and being a tool for studying the homeomorphism classification of 4-manifolds one could along familiar lines apply it to solve very interesting problems like the topological Poincare conjecture.