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The cohomology of the moduli space of controllable linear systems

The cohomology of the moduli space of controllable linear systems 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

The cohomology of the moduli space of controllable linear systems

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References (26)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/BF00047554
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: May 3, 2004

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