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|Title:||Generic Reductions of an Integrable G-Structure and an Infinitesimal Version of Cartan-Sternberg Reduction|
|Author(s):||Thomas, Mark Allen|
|Department / Program:||Mathematics|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|Abstract:||Given an integrable G-structure P and a closed subgroup H of G, we assign to each H-reduction of P a singular set in the base manifold. Our first main result is that generically, this singular set is a finite disjoint union of submanifolds (our theorem generalizes an unpublished result of L. Lipskie). The group can often be reduced even further off this singular set by a method of Cartan and Sternberg.
Motivated by the desire to obtain further transversality results concerning the Cartan-Sternberg reduction method, we give the beginning of an "infinitesimal" theory of Cartan-Sternberg reduction. Specifically, our second main result is that the method is well-defined on a certain set of jets of G-structures. Our third main result is that the reduction mapping thus obtained is smooth whenever the set of reducible jets is a manifold. (We conjecture that in general, this set is indeed a manifold).
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1983.
|Date Available in IDEALS:||2014-12-16|