Abstract
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Suppose
is a Heegaard split
compact orientable
–manifold
and
is a reducing
sphere for
.
Haken (1968) showed that there is then also a reducing sphere
for
the Heegaard splitting. Casson and Gordon (1987) extended the result to
–reducing disks in
and noted that in both
cases
is obtained from
by a sequence of operations
called
–surgeries. Here we show
that in fact one may take
.
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Keywords
Heegaard splitting, compression body, reducing disks and
spheres
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Mathematical Subject Classification
Primary: 57K35
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Publication
Received: 8 April 2020
Revised: 1 August 2022
Accepted: 16 August 2022
Published: 12 April 2024
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Publishers). Distributed under the Creative Commons
Attribution License 4.0 (CC BY). |
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