This 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 PhD'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. Several of the daytime history lectures also drew large
numbers of homology manifold participants. The interaction between the two
groups was very beneficial and should serve as a model for future such
We are grateful to the Oberwolfach Mathematics Institute for hosting the
meeting, and to the participants, authors and the referees for their
Frank Quinn and Andrew
Ranicki, August 2005