The free complex of a two-dimensional generalized convex shelling
نویسنده
چکیده
In this article, we study two open problems posed by Edelman & Reiner about topology of certain simplicial complexes associated with abstract convex geometries. As a special case, we concentrate on generalized convex shellings, which were introduced by Kashiwabara, Nakamura & Okamoto for their representation theorem of abstract convex geometries. We answer one of the problems affirmatively for 2-dimensional separable generalized convex shellings, and the other problem negatively already for this case.
منابع مشابه
Local topology of the free complex of a two-dimensional generalized convex shelling
A generalized convex shelling was introduced by Kashiwabara, Nakamura & Okamoto for their representation theorem of convex geometries. Motivated by the work by Edelman & Reiner, we study local topology of the free complex of a two-dimensional separable generalized convex shelling. As a result, we prove a deletion of an element from such a complex is homotopy equivalent to a single point or two ...
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