Cyclic homology is a mathematical concept in algebraic topology that generalizes homology theories to study algebras and their invariants through cyclic structures. It emerges from the study of noncommutative geometry and provides deep connections to various areas such as representation theory, number theory, and algebraic K-theory. The motivation for cyclic homology lies in understanding the behavior of algebras under cyclic permutations and the relationships between different cohomological techniques.
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