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We address a special case of the Stabilization Problem for Heegaard splittings, establishing an upper bound on the number of stabilizations required to make a Heegaard splitting of a Haken 3–manifold isotopic to an amalgamation along an essential surface. As a consequence we show that for any positive integer n there are 3–manifolds containing an essential torus and a Heegaard splitting such that the torus and splitting surface must intersect in at least n simple closed curves. These give the first examples of lower bounds on the minimum number of curves of intersection between an essential surface and a Heegaard surface that are greater than one.
Derby-Talbot, Ryan 1
@article{10_2140_agt_2009_9_811,
author = {Derby-Talbot, Ryan},
title = {Stabilization, amalgamation and curves of intersection of {Heegaard} splittings},
journal = {Algebraic and Geometric Topology},
pages = {811--832},
publisher = {mathdoc},
volume = {9},
number = {2},
year = {2009},
doi = {10.2140/agt.2009.9.811},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2009.9.811/}
}
TY - JOUR AU - Derby-Talbot, Ryan TI - Stabilization, amalgamation and curves of intersection of Heegaard splittings JO - Algebraic and Geometric Topology PY - 2009 SP - 811 EP - 832 VL - 9 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2009.9.811/ DO - 10.2140/agt.2009.9.811 ID - 10_2140_agt_2009_9_811 ER -
%0 Journal Article %A Derby-Talbot, Ryan %T Stabilization, amalgamation and curves of intersection of Heegaard splittings %J Algebraic and Geometric Topology %D 2009 %P 811-832 %V 9 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2009.9.811/ %R 10.2140/agt.2009.9.811 %F 10_2140_agt_2009_9_811
Derby-Talbot, Ryan. Stabilization, amalgamation and curves of intersection of Heegaard splittings. Algebraic and Geometric Topology, Tome 9 (2009) no. 2, pp. 811-832. doi: 10.2140/agt.2009.9.811
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