Generic Reductions of an Integrable G-Structure and an Infinitesimal Version of Cartan-Sternberg Reduction
Thomas, Mark Allen
This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/71209
Description
Title
Generic Reductions of an Integrable G-Structure and an Infinitesimal Version of Cartan-Sternberg Reduction
Author(s)
Thomas, Mark Allen
Issue Date
1983
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
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result is that generically, this singular set is a finite disjoint union of submanifolds (our theorem generalizes an unpublished result of L. Lipskie).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).
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
