此論文運用熱核方法，研究僅具有簡單固定點、且保持邊界的光滑映射在絕對和相對 de Rham 複形上的Lefschetz 固定點公式。通過同倫變形和構造參數熱核來推導公式，並同時考慮內部及邊界的固定點。我們的結果為 Lefschetz 固定點公式提供了熱核證明，闡釋邊界條件在 de Rham 複形上的作用。;In this thesis, we use the method of heat kernels to study the Lefschetz fixed point formula on absolute and relative de Rham complexes with respect to a smooth boundary-preserving map with simple fixed points only. We employ homotopy deformation and construct parametrix heat kernels to derive the formula, accounting for both interior and boundary fixed points. Our results provide a heat kernel proof of the Lefschetz fixed point formula, elucidating the role of boundary conditions in de Rham complexes.
