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Max Karoubi (changes) in nLab

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Max Karoubi is a French topologist, with main interests in algebraic and topological K-theory, cyclic (co)homology and noncommutative geometry à là Connes. He introduced the noncommutative differential forms to generalize the de Rham complex to noncommutative geometry.

Selected writings

Introducing what came to be known as Karoubi K-theory:

  • Max Karoubi, Espaces Classifiants en K-Théorie, Transactions of the American Mathematical Society 147 1 (Jan., 1970) 75-115 [[doi:10.2307/1995218]]

Introducing Hermitian K-theory:

  • Max Karoubi, Orlando Villamayor, K-théorie algébrique et K-théorie topologique II, Math. Scand. 32 (1973) 57-86 [[jstor:24490565](https://www.jstor.org/stable/24490565)]

  • Max Karoubi , §1 in:Le théorème de périodicité en K-théorie hermitienne , Quanta in of Maths1Quanta of Maths , AMS and Clay Math Mathematics Institute Proceesings Publications (2010) [[arXiv:0810.4707](https://arxiv.org/abs/0810.4707)]11, AMS and Clay Math Institute Publications (2010) 257-282 [[arXiv:0810.4707](https://arxiv.org/abs/0810.4707), pdf]

  • Max Karoubi, Mariusz Wodzicki, Algebraic and Hermitian K-theory of 𝒦\mathcal{K}-rings, The Quarterly Journal of Mathematics 64 3 (2013) 903–940 [[arXiv:1310.4123](https://arxiv.org/abs/1310.4123), doi:10.1093/qmath/hat030]

and topological Hermitian K-theory:

  • Max Karoubi, Périodicité de la K-théorie hermitienne, in: Hyman Bass (ed.), Algebraic K-Theory III – Hermitian K-Theory and Geometric Applications, Lecture Notes in Mathematics 343 (1973) 301-411 [[doi:10.1007/BFb0061366](https://doi.org/10.1007/BFb0061366)]

On topological K-theory:

  • Max Karoubi, K-Theory – An introduction, Grundlehren der mathematischen Wissenschaften 226, Springer 1978 (pdf, doi:10.1007%2F978-3-540-79890-3)

  • Lectures on K-theory, Proc. of the Trieste Conference in 2002, Contemporary Developments in Algebraic K-theory, ICTP Lecture notes 15 (2003).

On cyclic homology, topological K-theory and differential K-theory:

  • Max Karoubi, Homologie cyclique et K-théorie, Astérisque, no. 149 (1987) [[numdam:AST_1987__149__1_0](http://www.numdam.org/item/AST_1987__149__1_0)]

On algebraic topology and differential geometry:

  • Algebraic Topology via Differential Geometry (with Christian Leruste). Cambridge Univ. Press (1987), based on Méthodes de géométrie différentielle en topologie algébrique (1982, Paris 7)

On a form of Hodge-filtered differential topological K-theory:

  • Max Karoubi, Théorie générale des classes caractéristiques secondaires, K-Theory 4 1 (1990) 55-87 [[doi:10.1007/BF00534193](http://dx.doi.org/10.1007/BF00534193), pdf]

  • Max Karoubi, Classes Caractéristiques de Fibrés Feuilletés, Holomorphes ou Algébriques, in: Proceedings of Conference on Algebraic Geometry and Ring Theory in honor of Michael Artin, Part II (Antwerp 1992), K-Theory 8 2 (1994) 153-211 [[doi:10.1007/BF00961455](http://dx.doi.org/10.1007/BF00961455)]

On equivariant K-theory:

  • Max Karoubi, Equivariant K-theory of real vector spaces and real vector bundles, Topology and its Applications, 122, (2002) 531-456 (arXiv:math/0509497)

On KR-theory of algebraic varieties:

On Bott periodicity:

On twisted K-theory, Hermitian K-theory and KR-theory:

Last revised on November 16, 2023 at 06:59:58. See the history of this page for a list of all contributions to it.