Please use this identifier to cite or link to this item: https://research.matf.bg.ac.rs/handle/123456789/928
Title: Index of Grassmann manifolds and orthogonal shadows
Authors: Baralić, Djordje
Blagojević, Pavle V.M.
Karasev, Roman
Vučić, Aleksandar 
Affiliations: Topology 
Keywords: Cohomology of Grassmann manifolds;existence of equivariant maps;Fadell-Husseini ideal-valued index
Issue Date: 1-Nov-2018
Journal: Forum Mathematicum
Abstract: 
In this paper, we study the Z/2 action on the real Grassmann manifolds Gn (R2n) and ∼Gn (R2n) given by taking the (appropriately oriented) orthogonal complement.We completely evaluate the relatedZ/2 Fadell-Husseini index utilizing a novel computation of the Stiefel-Whitney classes of the wreath product of a vector bundle. These results are used to establish the following geometric result about the orthogonal shadows of a convex body: For n = 2a (2b + 1), k = 2a+1-1, a convex body C in R 2n, and k real-valued functions α1, . . . , αk continuous on convex bodies in R2n with respect to the Hausdorff metric, there exists a subspace V ⊆ R 2n such that projections of C to V and its orthogonal complement V have the same value with respect to each function αi, that is, αi(pV(C)) = αi(pV (C)) for all 1 ≤ i ≤ k.
URI: https://research.matf.bg.ac.rs/handle/123456789/928
ISSN: 09337741
DOI: 10.1515/forum-2018-0058
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