Dwyer’s filtration and topology of ${\mathbf 4}$-manifolds

Topological $4$-dimensional surgery is conjectured to fail, in general, for free fundamental groups. M. Freedman and P. Teichner have shown that surgery problems with an arbitrary fundamental group have a solution, provided they satisfy a certain condition on Dwyer’s filtration on second homology. We give a new geometric proof of this result, and analyze its relation to the canonical surgery problems.

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Published 1 January 2003