Abstract
We introduce the notion of weak slice for a homology 3-sphere or a knot in it in order to compute the Floer homology of topological imitations of a given homology 3-sphere. We obtain a qualitative result on the Floer homology. In particular, infinitely many hyperbolic homology 3-spheres with the same Floer homology are constructed as topological imitations of every given homology 3-sphere. The well-known connected sum and periodicity questions on the Floer homology are also discussed.
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