Homotopy invariance of AF-embeddability
  We prove that AF-embeddability is a homotopy invariant in the class of separable exact $C^*$-algebras. This work was inspired by Spielberg's work on homotopy invariance of AF-embeddability and Dadarlat's serial works on AF-embeddability of residually finite dimensional $C^*$-algebras. 
Narutaka Ozawa