Power operations in K-theory
Cohomology theories are invariants of spaces that are relatively computable while retaining much of the structure of a space. When a ring structure is present, some topological information is detected via the multiplication operation alone. Power operations are additional algebraic structures that a cohomology theory might have, and they have a particularly neat description in K-theory through an equivariant perspective. After a brief overview of cohomology operations and power operations in general, I will introduce equivariant K-theory, and use it to describe the power operations in K-theory. If there is time, I will try to address relationships with operations in other cohomology theories, as well as the relationship between power operations and spectra.
