Supermanifolds and Supergroups

Basic Theory

  • Gijs M. Tuynman

Part of the Mathematics and Its Applications book series (MAIA, volume 570)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Pages 141-201
  3. Pages 203-263
  4. Pages 265-334
  5. Pages 335-404
  6. Back Matter
    Pages 405-416

About this book


Supermanifolds and Supergroups explains the basic ingredients of super manifolds and super Lie groups. It starts with super linear algebra and follows with a treatment of super smooth functions and the basic definition of a super manifold. When discussing the tangent bundle, integration of vector fields is treated as well as the machinery of differential forms. For super Lie groups the standard results are shown, including the construction of a super Lie group for any super Lie algebra. The last chapter is entirely devoted to super connections.

The book requires standard undergraduate knowledge on super differential geometry and super Lie groups.


De Rham cohomology Lie algebra Lie group cohomology covariant derivative curvature differential geometry exterior derivative homology linear algebra manifold vector bundle

Authors and affiliations

  • Gijs M. Tuynman
    • 1
  1. 1.Université de Lille ILilleFrance

Bibliographic information