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Heegaard splittings of the form H + nK
Yoav Moriah, Saul Schleimer, Eric Sedgwick
Suppose that a three-manifold M contains infinitely many distinct strongly irreducible Heegaard splittings H + nK, obtained by Haken summing the surface H with n copies of the surf…
On the intersection of unknotting tunnels and the decomposing annulus in connected sums
Yoav Moriah
Given a Heegaard splitting of the complement of a composite knot $K=K_1# K_2$ in , where are prime knots, we have a unique, up to isotopy, decomposing…
A finiteness result for Heegaard splittings
Martin Lustig, Yoav Moriah
In this paper we show that for a given 3-manifold and a given Heegaard splitting there are finitely many preferred decomposing systems of disjoint essential disks. These a…
On boundary primitive manifolds and a theorem of Casson-Gordon
Yoav Moriah
In this paper it is shown that manifolds admitting minimal genus weakly reducible but irreducible Heegaard splittings contain an essential surface. This is an extension of a well k…
Connected sums of knots and weakly reducible Heegaard splittings
Yoav Moriah
This paper studies the question of whether minimal genus Heegaard splittings of exterior spaces of knots which are connected sums are weakly reducible or not. Furthermore it is sho…