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.
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:
On Bott periodicity:
On algebraic topology and differential geometry:
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