Geometrically Constructed Bases for Homology of Non-Crossing Partition Lattices

Details Geometrically Constructed Bases for Homology of Non-Crossing Partition Lattices Geometrically Constructed Bases for Homology of Non-Crossing Partition Lattices

2008-06-25

arxiv.org/abs/0806.4151v2

Mathematics

Combinatorics

9 pages, 1 figure Reference added

Scientific paper

For any finite, real reflection group $W$, we construct a geometric basis for the homology of the corresponding non-crossing partition lattice. We relate this to the basis for the homology of the corresponding intersection lattice introduced by Bj\"{o}rner and Wachs in \cite{BW} using a general construction of a generic affine hyperplane for the central hyperplane arrangement defined by $W$.

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