Heegaard splittings of (surface) x I are standars. Martin Scharlemann; Abigail Thompson — 1993 Mathematische Annalen
Unknotting Number, Genus, and Companion Tori. Martin Scharlemann; Abigail Thompson — 1988 Mathematische Annalen
Levelling an unknotting tunnel. Goda, Hiroshi; Scharlemann, Martin; Thompson, Abigail — 2000 Geometry & Topology