University of Illinois Urbana-Champaign

Complexity One Hamiltonian SU(2) and SO(3) Actions

Chiang, River

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/2142/86774

Description

Title
Complexity One Hamiltonian SU(2) and SO(3) Actions
Author(s)
Chiang, River
Issue Date
2001
Doctoral Committee Chair(s)
Susan Tolman
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
Language
eng
Abstract
Main Theorem. (Local Uniqueness over 0). Let G be SU(2) or SO(3). Let (M, o, phi), and (M', o', phi ') be six dimensional compact connected Hamiltonian G-manifolds such that 0 ∈ phi(M) = phi '(M'). There exists an invariant neighborhood V of 0 in g* over which the Hamiltonian G-manifolds are isomorphic if and only if (1) their Duistermaat-Heckman functions coincide; (2) their isotropy data and genus at 0 are the same; (3) if the zero fibers are tall with principal isotropy group S1, the first Stiefel-Whitney classes of phi-1(0) and phi '-1(0) in H1( Mreg0;Z2 ) and H1 ( M'reg0;Z2 ) are equal (under a proper identification of the reduced spaces at 0).
Graduation Semester
2001
Type of Resource
text
Permalink
http://hdl.handle.net/2142/86774

Owning Collections

Graduate Dissertations and Theses at Illinois PRIMARY
Graduate Theses and Dissertations at Illinois
Dissertations and Theses - Mathematics