在這個項目中，我們計劃研究具有邊界的複流形上的S^1-等變全純解析扭率和量子化跟約簡交換定理。這種方法是基於與中央研究院蕭欽玉博士，武漢大學李小山教授和中央研究院邵國寬博士最近的合作所發展的約簡至邊界的技術，在這合作項目中我們研究S^1等變指標定理和具有邊界的複流形上的摩斯不等式。本項目預計將我與蕭欽玉博士之前合作的柯西黎曼流形上的解析扭率和量子化跟約減交換定理的工作推廣到具有邊界的複流形上。我還計劃繼續與韓國仁荷大學李允源教授共同合作研究具有邊界的流形的精細解析扭率問題。我們計劃得出精細解析扭率是具有邊界的流形上的表現多樣體上的一個全純表示。 ;In this project we plan to study S^1-equivariant holomorphic analytic torsion and quantization commutes with reduction theorem on complex manifolds with boundary. The approach is based on certain reduction to boundary technique developed in a recent joint work with Chin-Yu Hsiao (Academia Sinica), Xiaoshan Li (Wuhan University) and Guokuan Shao (Academia Sinica) where we study S^1-equivariant index theorems and Morse inequalities on complex manifolds with boundary. This project will generalize my joint works with Chin-Yu Hsiao on analytic torsion and quantization commutes with reduction theorem on Cauchy-Riemann manifolds to complex manifolds with boundary. I also plan to continue my joint work with Yoonweon Lee, Inha University, Korea, on refined analytic torsion for manifolds with boundary. We plan to show that the refined analytic torsion is a holomorphic section over representation variety for manifolds with boundary.
