Geometric Integration Theory on Supermanifolds

Free Download Theodore Voronov, "Geometric Integration Theory on Supermanifolds"
English | 2014 | ISBN: 1904868827 | DJVU | pages: 0 | 1.7 mb
This volume provides a detailed account of the theory of forms and integration on supermanifolds a correct and nontrivial analogue of the Cartan de Rham theory based on new concepts. It also develops supermanifold differential topology including such notions as supermanifolds with boundary and supermanifold bordism, naturally arising for the needs of integration theory. One of key features is the identification of a class of proper morphisms of supermanifolds, intimately connected with the Berezin integration and of fundamental importance in various problems. The work starts from a concise introduction to superanalysis and supermanifolds. The author has managed to give an exposition free from algebraic formalism and which sets out afresh such challenging problems as the Berezin integral over a bounded domain. Applications are discussed, which include forms and spinors on manifolds, Radon transform, and an analytic proof of the Atiyah Singer theorem. The new edition includes an Appendix to present a current perspective on the original survey. The volume provides an excellent reference text for graduate students and researchers.

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