114 citations · 337 across the 39 of their papers we have counts for
40 papers
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.…