The higher homology of subsets of surfaces does not behave anomalously
by
Andreas Zastrow
University of Gdansk (Inst. Math.)

A talk is proposed on methods for how to prove that all higher singular homology groups of all subsets of surfaces vanish, with a 2^nd-countable topology of the surface being the only assumption and H₂ of closed surfaces being the only exception. The result should be understood as a result in the algebraic topology of non-tame spaces, and this is an area where many results for tame spaces do not hold. In particular, a wild two-dimensional complex with a non-trivial H₃ is known. On the other hand, the non-anomalous behaviour of higher homotopy groups and higher (singular) homology groups of subsets of the plane are former results of the author. While the extension from the plane to surfaces is not difficult in the homotopy case, it requires some work in the homology case, because homology groups are not invariant with respect to the covering space construction. Depending on the available time a talk might quickly sketch the relevant methods of the author's former results and then focus on the surgery techniques of wild maps that are the main tool for proving the new result as stated in the title-or it might just focus on some of the key-ideas for these proofs.

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Date received: May 21, 2001