Abstract
In this paper we consider the generalized Smith conjecture of codimension greater than two, which says that no periodic tranformation of Sl can have the tame knotted Sh as fixed point set if l-h>2 and h>3. Using the Brieskorn spheres, this paper gives the explicit counterexamples to show that the conjecture is false in the DIFF category for the following cases: (i) l-h is even more than 2 and l is odd; (ii) 2l≤3(h+1) and h+1≡0 (mod 4).
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