Differential KO-theory: Constructions, computations, and applications

We provide several constructions in differential KO-theory. First, we construct a refinement of the Aˆ-genus and pushforward leading to Riemann-Roch theorem. set up Atiyah-Hirzebruch spectral sequence (AHSS) for KO-theory explicitly identify differentials, including ones which mix geometric topological data. highlight power these explicit identifications by providing characterization forms image Pontrjagin character. Along way, fill gaps literature where K-theory is usually worked out leaving essentially untouched. also illustrate with examples applications, higher tangential structures, Adams operations, Wu formula.