Transgressions and Chern characters in coarse homotopy theory

Abstract: This paper investigates a variety of coarse homology theories and natural transformations between them. We in particular study the commutativity of a square relating analytical and topological transgressions with algebraic and homotopy theoretic Chern characters. Here a transgression is a natural transformation from a coarse homology theory to a functor which factorizes over the Higson corona functor, and a Chern character is a transformation from a $K$-theory like coarse or Borel-Moore type homology theory to an ordinary version.