Lectures on K-theory of toric manifolds and related spaces

These notes are intended to give a brief and informal introduction to the topology of torus manifolds. Our aim is to give an exposition of some recent results on the K-theory of smooth complete toric varieties and the closely related torus manifolds. Contents: §1. Toric varieties—basic notions and examples §2. Quasi-toric manifolds and torus manifolds §3. K-theory–basic concepts and some examples §4. K-theory of torus manifold