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There is a disk in S3 whose interior is PL embedded and whose boundary has a tame Cantor set of locally wild points, such that the n-fold cyclic coverings of S3 branched over the boundary of the disk are all S3. An uncountable set of inequivalent wild knots with these properties is exhibited.
We study analytic families of non-compact cycles, and prove there exists an analytic space of finite dimension, which gives a universal reparametrization of such a family, under some assumptions of regularity. Then we prove an analogous statement for meromorphic families of non-compact cycles. That is a new approach to Grauert’s results about meromorphic equivalence relations.
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