Pseudo-Anosov homeomorphisms which extend to orientation reversing homeomorphisms of \(S^ 3\) (Q1107878)

Infinitely many pseudo-Anosov homeomorphisms h of a closed surface \(F_ g\) of genus \(g>1\) are constructed which extend to the 3-sphere \(S^ 3\) exchanging the two complementary handle-bodies of the standard embedding of Fg in \(S^ 3\). As a consequence, identifying the boundaries of two copies of a handle-body of genus g by a power \(h^ n\) to obtain a Heegaard-splitting of a 3-manifold \(M_ n\), one obtains \(M_ n=S^ 3\), for n odd, and \(M_ n=\) the connected sum of g copies of \(S^ 2\times S^ 1\), for g even.