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math.GT2020
Generating the Goeritz group of
Martin Scharlemann
In 1980 J. Powell \cite{Po} proposed that five specific elements sufficed to generate the Goeritz group for any genus Heegaard splitting of the 3-sphere. Here we prove that a natur…
math.GT2020
Uniqueness in Haken's Theorem
Michael Freedman, Martin Scharlemann
Following Haken and Casson-Gordon, it was shown in [Sc] that given a reducing sphere or boundary-reducing disk E in a Heegaard split manifold M, the Heegaard surface T can be isoto…
math.GT2020★ 4 cited
A Strong Haken's Theorem
Martin Scharlemann
Suppose T is a Heegaard splitting surface for a compact orientable 3-manifold M, and S is a reducing sphere for M. In 1968 Haken showed that there is then also a reducing sphere S*…