Exotic homology manifolds (Oberwolfach 2003)

Abstract

AMS Classification Keywords PrefaceThis volume is the proceedings of the Mini-Workshop Exotic Homology manifolds held at Oberwolfach 29th June -5th July, 2003.Homology manifolds were developed in the first half of the 20th century to give a precise setting for Poincaré's ideas on duality. Major results in the second half of the century came from two different areas. Methods from the point-set tradition were used to study homology manifolds obtained by dividing genuine manifolds by families of contractible subsets. "Exotic" homology manifolds are ones that cannot be obtained in this way, and these have been investigated using algebraic and geometric methods.The Mini-Workshop brought together experts from the point-set and algebraic traditions, along with new Ph.D.s and people in related areas. There were 17 participants, 14 formal lectures and a problem session. There was a particular focus on the proof of the existence of exotic homology manifolds. This gave experts in each area an the opportunity to learn more about details coming from other areas. There had also been concerns about the stability ("shrinking") theorem that in retrospect is a crucial step in the proof but had not been worked out when the theorem was originally announced. This was discussed in detail. One of the high points of the conference was the discovery of a short and very general new proof of this result by Pedersen and Yamasaki (published in these proceedings), so there are now three independent treatments. Extensive discussions of examples and problems clarified the current state of the field and mapped out objectives for the next decade.A Mini-Workshop on history entitled "Henri Poincaré and topology" was held during the same week. There was joint discussion of the early history of manifolds, and each group offered evening lectures on topics of interest to the other.Copyright declaration is printed here 2 edited by