Some Sufficient Conditions for Heegaard Genera to Be Additive Under Annulus Sum

  • Fengling Li
  • Fengchun Lei
  • Guoqiu Yang

Abstract

Let $M_{i}$ be a compact orientable 3-manifold, and $A_{i}$ an incompressible annulus on a component $F_i$ of $\partial M_i$, $i=1,2$. Suppose $A_{1}$ is separating on $F_{1}$ and $A_{2}$ is non-separating on $F_{2}$. Let $M$ be the annulus sum of $M_1$ and $M_2$ along $A_1$ and $A_2$. In the present paper we show that if $M_{i}$ has a Heegaard splitting $V_{i}\cup_{S_{i}}W_{i}$ with Heegaard distance $d(S_{i})\geq2g(M_{i})+5$ for $i=1,2$, then $g(M)=g(M_{1})+g(M_{2})$. Moreover, when $g(F_{2})\geq 2$, the minimal Heegaard splitting of $M$ is unique up to isotopy.
Published
2014-12-03
How to Cite
Li, F., Lei, F., & Yang, G. (2014). Some Sufficient Conditions for Heegaard Genera to Be Additive Under Annulus Sum. MATHEMATICA SCANDINAVICA, 115(2), 173-188. https://doi.org/10.7146/math.scand.a-19221
Section
Articles