Diffeology

Released on by Patrick Iglesias-Zemmour
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  • Diffeology Book Detail

  • Author : Patrick Iglesias-Zemmour
  • Release Date : 2013-04-09
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 467
  • ISBN 13 : 0821891316
  • File Size : 24,24 MB
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Diffeology by Patrick Iglesias-Zemmour PDF Summary

Book Description: Diffeology is an extension of differential geometry. With a minimal set of axioms, diffeology allows us to deal simply but rigorously with objects which do not fall within the usual field of differential geometry: quotients of manifolds (even non-Hausdorff), spaces of functions, groups of diffeomorphisms, etc. The category of diffeology objects is stable under standard set-theoretic operations, such as quotients, products, co-products, subsets, limits, and co-limits. With its right balance between rigor and simplicity, diffeology can be a good framework for many problems that appear in various areas of physics. Actually, the book lays the foundations of the main fields of differential geometry used in theoretical physics: differentiability, Cartan differential calculus, homology and cohomology, diffeological groups, fiber bundles, and connections. The book ends with an open program on symplectic diffeology, a rich field of application of the theory. Many exercises with solutions make this book appropriate for learning the subject.

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