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The cohomology of the moduli space of controllable linear systems. (English) Zbl 0768.93009
Summary: We explicitly describe, by generators and relations, the cohomology ring of the manifold $$\Sigma_{n,m}({\mathbf F})$$ of controllable linear systems having $$m$$ inputs and state-space dimension $$n$$. It is shown that the cohomology ring of $$\Sigma_{n,m}({\mathbf F})$$ is isomorphic to the invariant cohomology ring of a product of projective spaces. Estimates for the cup length of the cohomology ring are obtained.

##### MSC:
 93B05 Controllability 93B27 Geometric methods 93C05 Linear systems in control theory 14D22 Fine and coarse moduli spaces 14F45 Topological properties in algebraic geometry 15A21 Canonical forms, reductions, classification
##### Keywords:
moduli spaces; Schubert calculus
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##### References:
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