kk-theory is an advanced concept in algebraic K-theory that specifically deals with the K-theory of C*-algebras and their homomorphisms. It provides a framework for understanding the relationships between different operator algebras and is pivotal in noncommutative geometry, where geometric concepts are applied in the context of noncommutative spaces. By studying kk-theory, one can gain insights into the structure of operator algebras and their representations, bridging the gap between algebra and geometry.
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