During my studies in university I have encountered several cohomology theories. Part of them I've met in topology\differential geometry\analysis on manifolds courses (simplicial, singular, cell, Alexander; de Rham), Gelfand-Fuks cohomology arised in variational calculus and in the theory of integrable systems, Čech cohomology appeared in my quantum mechanics course (Bohr-Sommerfeld quantisation condition), Dolbeault cohomology was useful in the complex analysis course. It seems that cohomology is now one of the broadly used toolboxes in the various fields (somehow related to geometry) of mathematics. Usefulness of cohomology theories is nicely described in this post on Math.SE. My question is about cohomology theories that arise in such fields directly related to geometry and variational calculus (and crossrelated) as convex analysis, optimal control/dynamical programming, set-valued analysis and differential inclusions. Studying these courses I haven't ever heard about any cohomology theory that arises in problems covered by these fields. I will be very thankful for any references to cohomology theories (if any exists) that were successfully applied within these disciplines.
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...utinam intelligere possim rationacinationes pulcherrimas quae e propositione concisa DE QUADRATUM NIHILO EXAEQUARI fluunt. (Henri Cartan)
[... if I could only understand the beautiful consequences following from the concise proposition $d^2=0$]
Georges Elencwajg
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