Geometric structures on finite- and infinite-dimensional Grassmannians
نویسندگان
چکیده
منابع مشابه
Geometric structures on finite- and infinite-dimensional Grassmannians
In this paper, we study the Grassmannian of n-dimensional subspaces of a 2n-dimensional vector space and its infinite-dimensional analogues. Such a Grassmannian can be endowed with two binary relations (adjacent and distant), with pencils (lines of the Grassmann space) and with so-called Zreguli. We analyse the interdependencies among these different structures. Mathematics Subject Classificati...
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Let Mn be a linear hyperplane arrangement in IR. We define finite posets Gk(M) and Vk(M) of oriented matroids associated with this, which approximate the Grassmannian Gk(IR) and the Stiefel manifold Vk(IR), respectively. The basic conjectures are that the “OM-Grassmannian” Gk(M) has the homotopy type of Gk(IR), and that the “OM-Stiefel bundle” ∆π : ∆Vk(M) −→ ∆Gk(M) is a surjective map. These co...
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ژورنال
عنوان ژورنال: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
سال: 2012
ISSN: 0138-4821,2191-0383
DOI: 10.1007/s13366-012-0096-4