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

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).

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Chiang, River

Contributors dc:contributor

• Susan Tolman

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3017043

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86774