Study Group on Topological K-Theory

We will overview different notions of positivity of vector bundles which include Griffiths positivity, Nakano positivity, Demailly positivity and algebro-geometric positivity. We will also discuss the relationship between these notions.

We will study curvatures on reductive homogeneous manifolds.

We will study $G$-invariant connections on reductive homogeneous manifolds.

We will review the construction of a left-invariant integrable almost complex structure on a Lie group $G$ via Samelson’s construction.

We will define characteristic classes in terms of the curvature of a connection. We will show that a characteristic classes is a cohomology class and independent of the choice of connection.

We will define characteristic classes in terms of the curvature of a connection. We will show that a characteristic classes is a cohomology class and independent of the choice of connection.

We will discuss the notion of curvature in the context of differential geometry and deduce the curvature tensor from the Levi-Civita connection.

We will follow Hatcher’s book on K-theory. The first meeting will be an organization meeting.