Geodesic
A strong Haken theorem
Scharlemann, Martin1
1 Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA, United States
Algebraic and Geometric Topology, Tome 24 (2024) no. 2, pp. 717-753

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

Suppose M = A ∪TB is a Heegaard split compact orientable 3–manifold and S ⊂ M is a reducing sphere for M. Haken (1968) showed that there is then also a reducing sphere S∗ for the Heegaard splitting. Casson and Gordon (1987) extended the result to ∂–reducing disks in M and noted that in both cases S∗ is obtained from S by a sequence of operations called 1–surgeries. Here we show that in fact one may take S∗ = S.

DOI : 10.2140/agt.2024.24.717
Keywords: Heegaard splitting, compression body, reducing disks and spheres

Scharlemann, Martin 1

1 Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA, United States 
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Scharlemann, Martin. A strong Haken theorem. Algebraic and Geometric Topology, Tome 24 (2024) no. 2, pp. 717-753. doi: 10.2140/agt.2024.24.717

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