鄭老師、蕭老師和蔡老師最近有一個定理，是在有 circle action 的 CR manifolds 上的 CR Riemann-Roch-Hirzebruch 定理。我們先複習在 Riemann surfaces 上的 Riemann-Roch-Hirzebruch 定理，然後再討論鄭老師、蕭老師和蔡老師在 CR manifolds 上 circle bundle 的 CR Riemann-Roch-Hirzebruch 定理。;In a recent paper of Cheng, Hsiao and Tsai, they obtained a CR Riemann-Roch-Hirzebruch Theorem for CR manifolds with a circle action. In this thesis we first review the Riemann-Roch-Hirzebruch Theorem for Riemann surfaces. Then we discuss CR Riemann-Roch-Hirzebruch Theorem of Cheng, Hsiao and Tsai for a circle bundle over a Riemann surface in details.
