The strong Haken theorem via sphere complexes
Algebraic and Geometric Topology, Tome 24 (2024) no. 5, pp. 2707-2719
Voir la notice de l'article provenant de la source Mathematical Sciences Publishers
We give a short proof of Scharlemann’s strong Haken theorem for closed 3–manifolds (and manifolds with spherical boundary). As an application, we also show that given a decomposing sphere R for a 3–manifold M that splits off an S2 × S1 summand, any Heegaard splitting of M restricts to the standard Heegaard splitting on the summand.
Keywords:
Heegaard splitting, Haken sphere, strong Haken theorem
Affiliations des auteurs :
Hensel, Sebastian 1 ; Schultens, Jennifer 2
@article{10_2140_agt_2024_24_2707,
author = {Hensel, Sebastian and Schultens, Jennifer},
title = {The strong {Haken} theorem via sphere complexes},
journal = {Algebraic and Geometric Topology},
pages = {2707--2719},
publisher = {mathdoc},
volume = {24},
number = {5},
year = {2024},
doi = {10.2140/agt.2024.24.2707},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.2707/}
}
TY - JOUR AU - Hensel, Sebastian AU - Schultens, Jennifer TI - The strong Haken theorem via sphere complexes JO - Algebraic and Geometric Topology PY - 2024 SP - 2707 EP - 2719 VL - 24 IS - 5 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.2707/ DO - 10.2140/agt.2024.24.2707 ID - 10_2140_agt_2024_24_2707 ER -
%0 Journal Article %A Hensel, Sebastian %A Schultens, Jennifer %T The strong Haken theorem via sphere complexes %J Algebraic and Geometric Topology %D 2024 %P 2707-2719 %V 24 %N 5 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.2707/ %R 10.2140/agt.2024.24.2707 %F 10_2140_agt_2024_24_2707
Hensel, Sebastian; Schultens, Jennifer. The strong Haken theorem via sphere complexes. Algebraic and Geometric Topology, Tome 24 (2024) no. 5, pp. 2707-2719. doi: 10.2140/agt.2024.24.2707
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