Let Sg denote the closed orientable surface of genus g. We construct exponentially many mapping class group orbits of collections of 2g+1 simple closed curves on Sg which pairwise intersect exactly once, extending a result of the first author [1] and further answering a question of Malestein, Rivin, and Theran [10]. To distinguish such collections up to the action of the mapping class group, we analyze their dual cube complexes in the sense of Sageev [12]. In particular, we show that for any even k between ⌊g/2⌋ and g, there exists such collections whose dual cube complexes have dimension k, and we prove a simplifying structural theorem for any cube complex dual to a collection of curves on a surface pairwise intersecting at most once.
Classification :
57-XX
Mots-clés :
Curves on surfaces, curve systems
Affiliations des auteurs :
Tarik Aougab
1
;
Jonah Gaster
2
1
Brown University, Providence, USA
2
Boston College, Chestnut Hill, USA
Tarik Aougab; Jonah Gaster. Curves intersecting exactly once and their dual cube complexes. Groups, geometry, and dynamics, Tome 11 (2017) no. 3, pp. 1061-1101. doi: 10.4171/ggd/422
@article{10_4171_ggd_422,
author = {Tarik Aougab and Jonah Gaster},
title = {Curves intersecting exactly once and their dual cube complexes},
journal = {Groups, geometry, and dynamics},
pages = {1061--1101},
year = {2017},
volume = {11},
number = {3},
doi = {10.4171/ggd/422},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/422/}
}
TY - JOUR
AU - Tarik Aougab
AU - Jonah Gaster
TI - Curves intersecting exactly once and their dual cube complexes
JO - Groups, geometry, and dynamics
PY - 2017
SP - 1061
EP - 1101
VL - 11
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/422/
DO - 10.4171/ggd/422
ID - 10_4171_ggd_422
ER -
%0 Journal Article
%A Tarik Aougab
%A Jonah Gaster
%T Curves intersecting exactly once and their dual cube complexes
%J Groups, geometry, and dynamics
%D 2017
%P 1061-1101
%V 11
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/422/
%R 10.4171/ggd/422
%F 10_4171_ggd_422
