nLab Max Karoubi

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.

• personal webpage;

• German wikipedia

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]

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

• Max Karoubi, Mariusz Wodzicki, Algebraic and Hermitian K-theory of $\mathcal{K}$-rings, The Quarterly Journal of Mathematics 64 3 (2013) 903–940 [arXiv: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]

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]

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, 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]

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:

• Max Karoubi, Charles Weibel, Algebraic and Real K-theory of Algebraic varieties, Topology 42 (2003) 715-742 [arXiv:math/0509412, doi:10.1016/S0040-9383(02)00069-1]

On Bott periodicity:

• Max Karoubi, Bott Periodicity in Topological, Algebraic and Hermitian K-Theory, in: Eric Friedlander, Daniel Grayson (eds.) Handbook of K-Theory, Springer (2005) [doi:10.1007/978-3-540-27855-9_4]

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

• Max Karoubi, Marco Schlichting, Charles Weibel, The Witt group of real algebraic varieties, Journal of Topology 9 4 (2016) 1257-1302 [arXiv:1506.03862, doi:10.1112/jtopol/jtw024]

• Max Karoubi, Charles Weibel, Twisted $K$-theory, Real $A$-bundles and Grothendieck–Witt groups, Journal of Pure and Applied Algebra 221 7 (2017) 1629-1640 [doi:10.1016/j.jpaa.2016.12.020]

Related entries

• Karoubian category (pseudo-abelian category)

• Karoubian envelope

• hyperbolic functor

category: people