Cyclic cohomology is a mathematical concept that arises in the fields of algebraic topology and non-commutative geometry. It provides a powerful tool for studying the algebraic structure and symmetries of various mathematical objects, such as rings, algebras, and group actions. In mathematics, cohomology is a branch of algebraic topology that assigns algebraic structures to topological spaces in order to capture their underlying symmetries. Cyclic cohomology extends this notion to non-commutative objects, where the order of operations matters.
The main idea behind cyclic cohomology is to study the invariants of cyclic permutations on algebraic structures. In other words, it seeks to understand the algebraic properties that remain unchanged under cyclic reordering. This is particularly useful in the study of non-commutative algebras and their associated geometric objects.
