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Powell's Conjecture on the Goeritz group of is stably true
Martin Scharlemann
In 1980 J. Powell proposed that, for every genus , five specific elements suffice to generate the Goeritz group of genus Heegaard splittings of . Powel…
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…
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…
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*…
One Powell generator is redundant
Martin Scharlemann
In 1980 J. Powell proposed that five specific elements sufficed to generate the Goeritz group of any Heegaard splitting of . This conjecture remains unresolved for genus $g \g…
Powell moves and the Goeritz group
Michael Freedman, Martin Scharlemann
In 1980 J. Powell proposed that five specific elements sufficed to generate the Goeritz group of any Heegaard splitting of , extending work of Goeritz on genus splittings.…