DISJOINT PAIRS OF ANNULI AND DISKS FOR HEEGAARD SPLITTINGS

Title & Authors
DISJOINT PAIRS OF ANNULI AND DISKS FOR HEEGAARD SPLITTINGS
SAITO TOSHIO;

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

대한수학회보, 2009. vol.46. 5, pp.1019-1029
1.
Parity criterion for unstabilized Heegaard splittings, Mathematical Proceedings of the Cambridge Philosophical Society, 2010, 149, 01, 115
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