For an arbitrary Coxeter group $W$, Reading and Speyer defined Cambrian semilattices $\mathcal{C}_{\gamma}$ as sub-semilattices of the weak order on $W$ induced by so-called $\gamma$-sortable elements. In this article, we define an edge-labeling of $\mathcal{C}_{\gamma}$, and show that this is an EL-labeling for every closed interval of $\mathcal{C}_{\gamma}$. In addition, we use our labeling to show that every finite open interval in a Cambrian semilattice is either contractible or spherical, and we characterize the spherical intervals, generalizing a result by Reading.
@article{10_37236_2910,
author = {Myrto Kallipoliti and Henri M\"uhle},
title = {On the topology of the {Cambrian} semilattices.},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {2},
doi = {10.37236/2910},
zbl = {1297.20039},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2910/}
}
TY - JOUR
AU - Myrto Kallipoliti
AU - Henri Mühle
TI - On the topology of the Cambrian semilattices.
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/2910/
DO - 10.37236/2910
ID - 10_37236_2910
ER -
%0 Journal Article
%A Myrto Kallipoliti
%A Henri Mühle
%T On the topology of the Cambrian semilattices.
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/2910/
%R 10.37236/2910
%F 10_37236_2910
Myrto Kallipoliti; Henri Mühle. On the topology of the Cambrian semilattices.. The electronic journal of combinatorics, Tome 20 (2013) no. 2. doi: 10.37236/2910
