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Let  f  be a periodic homeomorphism      M ↔  M M\, \leftrightarrow \,M      , where  M  is a compact connected 3-manifold (without boundary). Suppose that for each  i , the fixed-point set of      f i {f^i}       is a tame set. Then  f  is simplicial, relative to some triangulation of  M .

Statically tame periodic homeomorphisms of compact connected 3-manifolds. II. Statically tame implies tame