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Noncommutative Geometry Year 2000
Alain Connes
We describe basic concepts of noncommutative geometry and a general construction extending the familiar duality between ordinary spaces and commutative algebras to a duality betwee…
Noncommutative Manifolds the Instanton Algebra and Isospectral Deformations
Alain Connes, Giovanni Landi
We give new examples of noncommutative manifolds that are less standard than the NC-torus or Moyal deformations of $\Rb^n$. They arise naturally from basic considerations of noncom…
Renormalization in quantum field theory and the Riemann-Hilbert problem II: the -function, diffeomorphisms and the renormalization group
Alain Connes, Dirk Kreimer
We showed in part I (hep-th/9912092) that the Hopf algebra of Feynman graphs in a given QFT is the algebra of coordinates on a complex infinite dimensional Lie group …
A Short Survey of Noncommutative Geometry
Alain Connes
We give a survey of selected topics in noncommutative geometry, with some emphasis on those directly related to physics, including our recent work with Dirk Kreimer on renormalizat…
Cyclic Cohomology and Hopf Symmetry
Alain Connes, Henri Moscovici
Cyclic cohomology has been recently adapted to the treatment of Hopf symmetry in noncommutative geometry. The resulting theory of characteristic classes for Hopf algebras and their…