Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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DISJOINT PAIRS OF ANNULI AND DISKS FOR HEEGAARD SPLITTINGS

  • SAITO TOSHIO (Department of Mathematics Graduate School of Science Osaka University)
  • Published : 2005.07.01
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Abstract

We consider interesting conditions, one of which will be called the disjoint $(A^2,\;D^2)-pair$ property, on genus $g{\geq}2$ Heegaard splittings of compact orient able 3-manifolds. Here a Heegaard splitting $(C_1,\;C_2;\;F)$ admits the disjoint $(A^2,\;D^2)-pair$ property if there are an essential annulus Ai normally embedded in $C_i$ and an essential disk $D_j\;in\;C_j((i,\;j)=(1,\;2)\;or\;(2,\;1))$ such that ${\partial}A_i$ is disjoint from ${\partial}D_j$. It is proved that all genus $g{\geq}2$ Heegaard splittings of toroidal manifolds and Seifert fibered spaces admit the disjoint $(A^2,\;D^2)-pair$ property.

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Cited by

  1. Parity criterion for unstabilized Heegaard splittings vol.149, pp.01, 2010, https://doi.org/10.1017/S0305004110000095