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Non-crossing partitions and Milnor fibers

Autor: Brady, Thomas, Falk, Michael, Watt, Colum

Publikováno v: Algebr. Geom. Topol. 18 (2018) 3821-3838

For a finite real reflection group $W$ we use non-crossing partitions of type $W$ to construct finite cell complexes with the homotopy type of the Milnor fiber of the associated $W$-discriminant $\Delta_W$ and that of the Milnor fiber of the defining

Externí odkaz: http://arxiv.org/abs/1709.07811

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From Permutahedron to Associahedron

Autor: Brady, Thomas, Watt, Colum

For each finite real reflection group $W$, we identify a copy of the type-$W$ simplicial generalised associahedron inside the corresponding simplicial permutahedron. This defines a bijection between the facets of the generalised associahedron and the

Externí odkaz: http://arxiv.org/abs/0804.2331

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h-vectors of generalized associahedra and non-crossing partitions

Autor: Athanasiadis, Christos A., Brady, Thomas, McCammond, Jon, Watt, Colum

A case-free proof is given that the entries of the $h$-vector of the cluster complex $\Delta (\Phi)$, associated by S. Fomin and A. Zelevinsky to a finite root system $\Phi$, count elements of the lattice $\nc$ of noncrossing partitions of correspond

Externí odkaz: http://arxiv.org/abs/math/0602293

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Shellability of noncrossing partition lattices

Autor: Athanasiadis, Christos A., Brady, Thomas, Watt, Colum

We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type $D_n$ and those of exceptional type and rank at least

Externí odkaz: http://arxiv.org/abs/math/0503007

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Lattices in finite real reflection groups

Autor: Brady, Thomas, Watt, Colum

For a finite real reflection group $W$ with Coxeter element $\gamma$ we give a uniform proof that the closed interval, $[I, \gamma]$ forms a lattice in the partial order on $W$ induced by reflection length. The proof involves the construction of a si

Externí odkaz: http://arxiv.org/abs/math/0501502

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