Infinite-dimensional supermanifolds, lie supergroups and the supergroup of superdiffeomorphisms / von Jakob Schütt ; [Betreuer: Prof. Dr. Helge Glöckner (Universität Paderborn), Prof. Dr. Joachim Hilgert (Universität Paderborn), Prof. Dr. Wolfgang Bertram (Université de Lorraine)]. Paderborn, 2019
Inhalt
- Acknowledgements
- Abstract
- Introduction
- Preliminaries and Notation
- Partitions
- The Category of Grassmann Algebras
- Locally Convex Manifolds
- Categories
- Linear Superspaces and Superalgebras
- Supermanifolds
- Open Subfunctors
- Superdomains
- Supermanifolds
- Batchelor's Theorem
- Super Vector Bundles
- The Tangent Bundle of a Supermanifold
- Lie Supergroups
- The Lie Superalgebra of a Lie Supergroup
- Trivializations and the Exponential Map
- Super Harish-Chandra Pairs
- Lie Supergroups with a Smooth Exponential Map
- Examples
- Superdiffeomorphisms
- Spaces of Sections of Super Vector Bundles
- The Automorphism Group of a Supermanifold
- The Functor of Supermorphisms and Superdiffeomorphisms
- The Supergroup of Superdiffeomorphisms
- Important Facts
- Multilinear Bundles
- Polynomial Groups
- The Lie Group of Vector Bundle Automorphisms
- The Lie Group Structure of the Gauge Group
- The Lie Group Structure of the Diffeomorphism Group
- The Automorphism Group
- Higher Order Tangent Groups
- Higher Order Tangent Lie Groups
- Higher Order Diffeomorphism Groups
- Higher Order Bundle Automorphism Groups
- References
- Symbols
- Index