Geodesic
On the Topology of the Cambrian Semilattices
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013).

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For an arbitrary Coxeter group $W$, David Speyer and Nathan Reading defined Cambrian semilattices $C_{\gamma}$ as certain sub-semilattices of the weak order on $W$. In this article, we define an edge-labelling using the realization of Cambrian semilattices in terms of $\gamma$-sortable elements, and show that this is an EL-labelling for every closed interval of $C_{\gamma}$. In addition, we use our labelling 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 Nathan Reading. 
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     author = {Kallipoliti, Myrto and M\"uhle, Henri},
     title = {On the {Topology} of the {Cambrian} {Semilattices}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)},
     year = {2013},
     doi = {10.46298/dmtcs.2320},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2320/}
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Kallipoliti, Myrto; Mühle, Henri. On the Topology of the Cambrian Semilattices. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013). doi : 10.46298/dmtcs.2320. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2320/

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