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Geometric and Lie-theoretic principles in pure and applied deformation theory. (English) Zbl 0685.58038
Deformation theory of algebras and structures and applications, Nato Adv. Study Inst., Castelvecchio-Pascoli/Italy 1986, Nato ASI Ser., Ser. C 247, 701-796 (1988).
[For the entire collection see Zbl 0654.00006.]
Author’s summary: “These notes develop a geometric point of view in the theory of deformation of structures, emphasizing the role of the orbit space of a group of symmetries of a system of differential equations acting on the space of solutions. The usual infinitesimal deformation space which appears as a cohomology group in many special situations is the tangent space to this space of orbits. The classical theory of deformation of complex structures is presented first as a model, then the deformation of the Cartan-Maurer equations is discussed from a differential point of view, leading in a very natural way to Chevalley- Eilenberg cohomology. Relations with certain aspects of mathematical physics and control theory are evident.”
Reviewer: A.Verona
MSC:
58H15 Deformations of general structures on manifolds
32G05 Deformations of complex structures