Supermanifolds: Theory and Applications

The subject of supermanifolds has to some extent ‘just growed’ like Topsy, as the idea of adjoining anticommuting variables to conventional commuting variables proved useful in a variety of contexts. This has led to a bewildering variety of approaches which has often obscured the underlying unity of the ideas. Supermanifolds have been with me through much of this period of growth, and now in writing this book I intend not a formal mathematical treatise, but rather a working man or woman’s guide to the geometry and analysis of supermanifolds, together with applications of the theory. Supermanifolds continue to find new uses, the underlying ideas have proved robust, powerful and adaptable. My aim is to provide a unified picture, distilling the key ideas from a welter of sources. I have tried to give references to relevant original work, and can only apologise for any failures, which will have been unintentional.