Supermanifolds and Supergroups

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

From the reviews:

"The author provides an introduction to the theory of supermanifolds … . The book is written in a logical order and it is self-contained. … The list of references indicates also where in the book the reference is quoted. Therefore, I find this book very useful, a true instrument of reference and study. It can be read by graduate students in mathematics and physics and by anyone interested in this subject and it presents in very pleasant and accessible manner all the basics … ." (Eugen Pascu, Zentralblatt MATH, Vol. 1083 (9), 2006)

"This book is an introduction to super differential geometry at the level of graduate studies in mathematics and theoretical physics. … the book presents in a clear and precise way difficult notions and theories about supermanifolds and supergroups. It will be easily readable by the people for whom it is intended, i.e. graduate students in mathematics and theoretical physics … . It is self-contained … . the book will be very useful for both beginners and active researchers in the field of supermanifolds and supergroups." (Anargyros Fellouris, Mathematical Reviews, Issue 2005 k)

• Université de Lille I, Lille, France

  Gijs M. Tuynman

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