On the stratification of the orbit space for the action of automorphisms on connections

Witold Kondracki ; Jan Rogulski

GDML_Books, (1986), p.

Résumé

CONTENTSIntroduction..................................................................................................................................................5§1. Basic notions and notation.....................................................................................................................7  1.1. Automorphisms of principal bundles....................................................................................................7  1.2. Connections and parallel translations.................................................................................................9  1.3. Symmetries and connections.............................................................................................................11§2. The action of the gauge group on connections....................................................................................14  2.1. The gauge group...............................................................................................................................14  2.2. The action of on $G^{k+1}$ on $C^k$................................................................................................17  2.3. Weak and strong invariant metrics on $C^k$.....................................................................................20  2.4. The equivariant embedding of $C^k$ into the space of $H^k$ Riemannian metrics on P...................23§3. The Slice Theorem...............................................................................................................................30  3.1. The Hodge-Kodaira-like decomposition for $T_e Φ_A$....................................................................30  3.2. The orbits are submanifolds..............................................................................................................36  3.3. The Slice Theorem............................................................................................................................38§4. The geometric structure of $R^k = C^k/G^{k+1}$..................................................................................43  4.1. Consequences of the Slice Theorem.................................................................................................44  4.2. The Countability Theorem.................................................................................................................47  4.3. Density theorems...............................................................................................................................49  4.4. The stratification of $R^k$.................................................................................................................57References.................................................................................................................................................61

Détail

Zbl 0614.57025

EUDML-ID : urn:eudml:doc:268369