TY - JOUR
T1 - A geometric duality for order complexes and hyperplane complements
AU - Falk, Michael
N1 - Funding Information:
This work was partially supported by NSF grant DMS-9004202 and an NAU Organized Research grant.
PY - 1992/9
Y1 - 1992/9
N2 - The top cohomology of the complement of an arrangement of complex hyperplanes is canonically isomorphic to the order homology of the associated intersection lattice. We put this result into a geometric framework by constructing a realization of the order complex of the intersection lattice inside the link of the arrangement. The canonical isomorphism is shown to coincide with the restriction of the classical Alexander duality mapping. Thus the isomorphism is a consequence of the linking of (l - 2)-spheres and l-tori in the (2l - 1)-sphere.
AB - The top cohomology of the complement of an arrangement of complex hyperplanes is canonically isomorphic to the order homology of the associated intersection lattice. We put this result into a geometric framework by constructing a realization of the order complex of the intersection lattice inside the link of the arrangement. The canonical isomorphism is shown to coincide with the restriction of the classical Alexander duality mapping. Thus the isomorphism is a consequence of the linking of (l - 2)-spheres and l-tori in the (2l - 1)-sphere.
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U2 - 10.1016/S0195-6698(05)80014-9
DO - 10.1016/S0195-6698(05)80014-9
M3 - Article
AN - SCOPUS:38249008866
SN - 0195-6698
VL - 13
SP - 351
EP - 356
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
IS - 5
ER -