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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...

A canonically defined mod 2 linear dependency current is associated to each collection v of sections, Vl, . . . , Vm, of a real rank n vector bundle. This current is supported on the linear dependency set of v. It is defined whenever the collection v satisfies a weak measure theoretic condition called "atomicity." Essentially any reasonable collection of sections satisfies this condition, vastl...

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.

We develop Stiefel-Whitney classes for coherent real analytic sheaves and investigate their applications to analytic cycles on real analytic manifolds.

The aim of this paper is to present a new class of learning models for linear as well as non-linear neural layers called Orthonormal StronglyConstrained (SOC or Stiefel). They allow to solve orthonormal problems where orthonormal matrices are involved. After general properties of the learning rules belonging to this new class are shown, examples derived independently or by reviewing learning th...

We calculate from first principles the motivic cohomology of Gl(n) and Stiefel manifoldsW(n,m). We also demonstrate a comparison map ΣtP → Gl(n). CONTENTS