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Thomas, Mark Allen 2014-12-16T06:18:04Z 2014-12-16T06:18:04Z 10000-01-01 1983 1983 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result is that generically, this singular set is a finite disjoint union of submanifolds (our theorem generalizes an unpublished result of L. Lipskie).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). Made available in DSpace on 2014-12-16T06:18:04Z (GMT). No. of bitstreams: 1 8324657.pdf: 2582771 bytes, checksum: 71cd0e404207758ff28c8a00a744dba0 (MD5) Previous issue date: 1983 Embargo set by: Seth Robbins for item 71375 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 92 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1983. http://hdl.handle.net/2142/71209 (UMI)AAI8324657 Mathematics Generic Reductions of an Integrable G-Structure and an Infinitesimal Version of Cartan-Sternberg Reduction text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.