Comments:

124 pages,

Abstract:

This concise book covers the following topics of noncommutative geometry: "1. Introduction 2. Morita equivalence 3. Derivations and Atiyah algebras 4. The Bar complex 5. Hochschild homology and cohomology 6. Poisson brackets and Gerstenhaber algebras 7. Deformation quantization 8. Kahler differentials 9. The Hochschild--Kostant--Rosenberg Theorem 10. Noncommutative differential forms 12. Noncommutative Calculus 13. The Representation functor 14. Double-derivations and the double tangent bundle 15. Noncommutative symplectic geometry 16. Kirillov--Kostant bracket 17. Review of (commutative) Chern--Weil theory 18. Noncommutative Chern--Weil theory 19. Chern character in K--theory 20. Formally smooth algebras 21. Serre functors and duality 22. Geometry over an operad" Two related files under the GNU license are added that focus on the potential physical applications of NCG.

Rights:

Open access: http://arxiv.org/PS_cache/math/pdf/0506/0506603v1.pdf

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