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Abstract: Let two Heegaard splittings $V 1 \cup W 1$ and $V 2 \cup W 2$ of a 3-manifold$M$ be given. We consider the union stabilization $M=V \cup W$ which is acommon stabilization of $V 1 \cup W 1$ and $V 2 \cup W 2$ having the propertythat $V=V 1 \cup V 2$. We show that any two Heegaard splittings of a 3-manifoldhave a union stabilization. We also give some examples with numerical bounds onthe minimal genus of union stabilization. On the other hand, we give an exampleof a candidate for which the minimal genus of union stabilization is strictlylarger than the usual stable genus - the minimal genus of commonstabilization.



Author: Jung Hoon Lee

Source: https://arxiv.org/







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