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This volume is an introductory textbook to K-theory, both algebraic
and topological, and to various current research topics within the
field, including Kasparov's bivariant K-theory, the Baum-Connes
conjecture, the comparison between algebraic and topological
K-theory of topological algebras, the K-theory of schemes, and the
theory of dg-categories.
This volume contains the proceedings of the ICM 2018 satellite
school and workshop $K$-theory conference in Argentina. The school
was held from July 16-20, 2018, in La Plata, Argentina, and the
workshop was held from July 23-27, 2018, in Buenos Aires,
Argentina. The volume showcases current developments in $K$-theory
and related areas, including motives, homological algebra, index
theory, operator algebras, and their applications and connections.
Papers cover topics such as $K$-theory of group rings, Witt groups
of real algebraic varieties, coarse homology theories, topological
cyclic homology, negative $K$-groups of monoid algebras, Milnor
$K$-theory and regulators, noncommutative motives, the
classification of $C^*$-algebras via Kasparov's $K$-theory, the
comparison between full and reduced $C^*$-crossed products, and a
proof of Bott periodicity using almost commuting matrices.
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