This Thursday at 12:00, U. Haifa Topology & Geometry seminar on Jun 6, 2019
Geometry & Topology Seminar
Speaker: Chaim Schochet (Technion)
Topic: What is K-theory for C*-algebras and why should topologists care about it
Place: Room 614 in the Science & Education Building
Date: Thursday, Jun 6, 2019
Topological K-theory for C^*-algebras is a generalization of classical K-theory for compact spaces. It has proven to be an invaluable tool in several areas of functional analysis and mathematical physics. It turns out that it is also very useful for some problems in classical topology. In this expository talk we will outline the basic properties of K-theory and show how it has been applied to develop tools and solve problems that are out of reach by classical algebraic topological methods.
Here’s a sample. If a finite (or compact) group G acts on a compact space X then topologists routinely study the space of orbits X/G and use tools such as equivariant K-theory. But what if the group G is not compact? What if it is the integers, so the action is given by a homeomorphism X to X, and suppose that the orbit of every point is dense in X. Then every point is dense in X/G. What classical tools can be used on such a space?