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An Introduction to Noncommutative Geometry

Mathematical Physics 2008-11-06 v2 High Energy Physics - Theory Differential Geometry math.MP Quantum Algebra

Abstract

This is the introduction and bibliography for lecture notes of a course given at the Summer School on Noncommutative Geometry and Applications, sponsored by the European Mathematical Society, at Monsaraz and Lisboa, Portugal, September 1-10, 1997. In the published version, an epilogue of recent developments and many new references from 1998-2006 have been added. 1. Commutative geometry from the noncommutative point of view. 2. Spectral triples on the Riemann sphere. 3. Real spectral triples, the axiomatic foundation. 4. Geometries on the noncommutative torus. 5. The noncommutative integral. 6. Quantization and the tangent groupoid. 7. Equivalence of geometries. 8. Action functionals. 9. Epilogue: new directions.

Keywords

Cite

@article{arxiv.physics/9709045,
  title  = {An Introduction to Noncommutative Geometry},
  author = {Joseph C. Varilly},
  journal= {arXiv preprint arXiv:physics/9709045},
  year   = {2008}
}

Comments

18 pages, LaTeX, updated bibliography (only). The full document is now published in the EMS Series of Lectures in Mathematics