Voir la notice de l'article provenant de la source Mathematical Sciences Publishers
Let S be a closed orientable surface of genus at least 2. The action of an automorphism f on the curve complex of S is an isometry. Via this isometric action on the curve complex, a translation length is defined on f. The geometry of the mapping torus Mf depends on f. As it turns out, the structure of the minimal-genus Heegaard splitting also depends on f: the canonical Heegaard splitting of Mf, constructed from two parallel copies of S, is sometimes stabilized and sometimes unstabilized. We give an example of an infinite family of automorphisms for which the canonical Heegaard splitting of the mapping torus is stabilized. Interestingly, complexity bounds on f provide insight into the stability of the canonical Heegaard splitting of Mf. Using combinatorial techniques developed on 3–manifolds, we prove that if the translation length of f is at least 8, then the canonical Heegaard splitting of Mf is unstabilized.
Keywords: Heegaard splitting, stabilization, mapping torus, translation length
Zou, Yanqing 1
@article{10_2140_agt_2017_17_3435,
author = {Zou, Yanqing},
title = {The unstabilized canonical {Heegaard} splitting of a mapping torus},
journal = {Algebraic and Geometric Topology},
pages = {3435--3448},
publisher = {mathdoc},
volume = {17},
number = {6},
year = {2017},
doi = {10.2140/agt.2017.17.3435},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2017.17.3435/}
}
TY - JOUR AU - Zou, Yanqing TI - The unstabilized canonical Heegaard splitting of a mapping torus JO - Algebraic and Geometric Topology PY - 2017 SP - 3435 EP - 3448 VL - 17 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2017.17.3435/ DO - 10.2140/agt.2017.17.3435 ID - 10_2140_agt_2017_17_3435 ER -
%0 Journal Article %A Zou, Yanqing %T The unstabilized canonical Heegaard splitting of a mapping torus %J Algebraic and Geometric Topology %D 2017 %P 3435-3448 %V 17 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2017.17.3435/ %R 10.2140/agt.2017.17.3435 %F 10_2140_agt_2017_17_3435
Zou, Yanqing. The unstabilized canonical Heegaard splitting of a mapping torus. Algebraic and Geometric Topology, Tome 17 (2017) no. 6, pp. 3435-3448. doi: 10.2140/agt.2017.17.3435
Cité par Sources :