On continuous maps between Grassmann manifolds

Korbaš, J. ; Sankaran, P. (1991) On continuous maps between Grassmann manifolds Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 101 (2). pp. 111-120. ISSN 0253-4142

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Official URL: http://www.ias.ac.in/j_archive/mathsci/101/2/111-1...

Related URL: http://dx.doi.org/10.1007/BF02868020

Abstract

Let G n,k denote the Grassmann manifold of k-planes in Rn. We show that for any continuous map f: G n,k→Gn,l the induced map inZ/2-cohomology is either zero in positive dimensions or has image in the subring generated by w1n, k), provided 1≤l≤k≤[n/2] andn≥k+2l-1. Our main application is to obtain negative results on the existence of equivariant maps between oriented Grassmann manifolds. We also obtain positive results in many cases on the existence of equivariant maps between oriented Grassmann manifolds.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Grassmann Manifolds; Steenrod Squares; Stiefel-Whitney Classes; Equivariant Maps
ID Code:57712
Deposited On:29 Aug 2011 08:22
Last Modified:18 May 2016 09:01

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