# Algebraic K-theory of topological algebras

Algebra/Geometry/Topology Seminar

#### by Snigdhayan Mahanta

Abstract: The abstract machinery of Quillen's algebraic K-theory can be used to recover the topological K-theory of spaces by applying it to specific topological algebras. I shall begin with a brief introduction to algebraic and topological K-theory. The traditional approach to algebraic K-theory (for algebras) requires the input algebra to be unital. Quillen generalized the situation by creating a new $$K_0'$$-theory for nonunital algebras. I shall explain the construction of higher K'-theory and show how it is related to topological K-theory.