We provide an algorithm to determine the Heegaard genus of simple 3–manifolds with nonempty boundary. More generally, we supply an algorithm to determine (up to ambient isotopy) all the Heegaard splittings of any given genus for the manifold. As a consequence, the tunnel number of a hyperbolic link is algorithmically computable. Our techniques rely on Rubinstein’s work on almost normal surfaces, and also on a new structure called a partially flat angled ideal triangulation.
Lackenby, Marc 1
@article{10_2140_agt_2008_8_911,
author = {Lackenby, Marc},
title = {An algorithm to determine the {Heegaard} genus of simple 3{\textendash}manifolds with nonempty boundary},
journal = {Algebraic and Geometric Topology},
pages = {911--934},
year = {2008},
volume = {8},
number = {2},
doi = {10.2140/agt.2008.8.911},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2008.8.911/}
}
TY - JOUR AU - Lackenby, Marc TI - An algorithm to determine the Heegaard genus of simple 3–manifolds with nonempty boundary JO - Algebraic and Geometric Topology PY - 2008 SP - 911 EP - 934 VL - 8 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2008.8.911/ DO - 10.2140/agt.2008.8.911 ID - 10_2140_agt_2008_8_911 ER -
%0 Journal Article %A Lackenby, Marc %T An algorithm to determine the Heegaard genus of simple 3–manifolds with nonempty boundary %J Algebraic and Geometric Topology %D 2008 %P 911-934 %V 8 %N 2 %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2008.8.911/ %R 10.2140/agt.2008.8.911 %F 10_2140_agt_2008_8_911
Lackenby, Marc. An algorithm to determine the Heegaard genus of simple 3–manifolds with nonempty boundary. Algebraic and Geometric Topology, Tome 8 (2008) no. 2, pp. 911-934. doi: 10.2140/agt.2008.8.911
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