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In this paper we explicitly describe, by generators and relations, the cohomology ring of the manifold ∑ n,m (F) of controllable linear systems having m inputs and state-space dimension n. It is shown that the cohomology ring of ∑ n,m (F) is isomorphic to the invariant cohomology ring of a product of projective spaces. Estimates for the cup length of the cohomology ring are obtained.
Acta Applicandae Mathematicae – Springer Journals
Published: May 3, 2004
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