Chern maps for U-theory Original Research Article

For an exact k-linear category image with a duality functor, the dihedral homology of image is defined. We show that when image, the image of the generalized Chern map from the U-theory of image to cyclic homology, lies in a direct summand which is the dihedral homology of image. When image is the category of finitely generated projective A-modules over a k-algebra A, we recover the early results of Cortinas (1993) and Lodder (1992). The approach we adopt here is more categorical, inspired by McCarthyʹs work (1992).