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Abstract Let $$N_k$$ N k denote the closed non-orientable surface of genus k . In this paper we study behaviour ‘square map’ from group isometries hyperbolic 3-space to subgroup orientation preserving isometries. The properties and other related maps serve as a technica...

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...

The Stiefel manifolds < are shown to be non-neutral for m*5, 2 #2)k"2l( 2 !2. 2001 Elsevier Science Ltd. All rights reserved.