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

Witold Kondracki; Jan Rogulski

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1986

Abstract

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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

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Witold Kondracki, and Jan Rogulski. On the stratification of the orbit space for the action of automorphisms on connections. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1986. <http://eudml.org/doc/268369>.

@book{WitoldKondracki1986,
abstract = {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},
author = {Witold Kondracki, Jan Rogulski},
keywords = {orbit space of the action of the gauge group; smooth principal G-bundle; compact Lie group; space of smooth connections; stratification; Hilbert- Lie group; existence of tubular neighborhoods for the action; holonomy bundle; configuration space for Yang-Mills field theory},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {On the stratification of the orbit space for the action of automorphisms on connections},
url = {http://eudml.org/doc/268369},
year = {1986},
}

TY - BOOK
AU - Witold Kondracki
AU - Jan Rogulski
TI - On the stratification of the orbit space for the action of automorphisms on connections
PY - 1986
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - 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
LA - eng
KW - orbit space of the action of the gauge group; smooth principal G-bundle; compact Lie group; space of smooth connections; stratification; Hilbert- Lie group; existence of tubular neighborhoods for the action; holonomy bundle; configuration space for Yang-Mills field theory
UR - http://eudml.org/doc/268369
ER -

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