Birkhoff-Grothendieck定理

On geometry behind Birkhoff theorem

This is an elementary geometrical proof of Birkhoff theorem. It is hardly important, but the pictures behind are quite nice.

A condensed proof of the differential Grothendieck-Riemann-Roch theorem

We give a direct proof that the Freed-Lott differential analytic index is well defined and a condensed proof of the differential Grothendieck-Riemann-Roch theorem. As a byproduct we also obtain a direct proof that the R/Z analytic index is well defined and a condensed proof of the R/Z Grothendieck-Riemann-Roch theorem.

复平坦向量丛的局部指标理论与Riemann-Roch-Grothendieck定理 II

Local index theory and the Riemann-Roch-Grothendieck theorem for complex flat vector bundles II

该研究在微分形式层面证明了复平坦向量丛的Riemann-Roch-Grothendieck定理的实部，推进了相关局部指标理论研究。

The flat Grothendieck-Riemann-Roch theorem without adiabatic techniques

In this paper we give a simplified proof of the flat Grothendieck-Riemann-Roch theorem. The proof makes use of the local family index theorem and basic computations of the Chern-Simons form. In particular, it does not involve any adiabatic limit computation of the reduced eta-invariant.

超曲面数据：一般性质与球对称下的Birkhoff定理

Hypersurface data: General properties and Birkhoff theorem in spherical symmetry

本文研究了度量超曲面数据的一般几何性质，在球对称情形下引入规范不变量与径向协变导数，将Einstein场方程约束方程紧凑化，并推导出抽象超曲面设定下真空情形的Birkhoff定理推广。

Local index theory and the Riemann-Roch-Grothendieck theorem for complex flat vector bundles

The purpose of this paper is to give a proof of the real part of the Riemann-Roch-Grothendieck theorem for complex flat vector bundles at the differential form level in the even dimensional fiber case. The proof is, roughly speaking, an application of the local family index theorem for a perturbed twisted spin Dirac operator, a variational formula of the Bismut-Cheeger eta form without the kernel bundle assumption in the even dimensional fiber case, and some properties of the Cheeger-Chern-Simons class of complex flat vector bundle.