Logarithmic forms with twisted coefficients

关于$V$-扭曲Higgs包在穿孔曲线上的对数谱对应

Logarithmic spectral correspondence for $V$--twisted Higgs bundles on punctured curves

研究了穿孔曲线上的$V$-扭曲Higgs包的对数性质，通过Hecke紧致化方法分类了此类包，并扩展了ABK的谱对应理论到穿孔情况。

Meromorphic differentials with twisted coefficients on compact Riemann surfaces

This note is to concern a generalization to the case of twisted coefficients of the classical theory of Abelian differentials on a compact Riemann surface. We apply the Dirichlet's principle to a modified energy functional to show the existence of differentials with twisted coefficients of the second and third kinds under a suitable assumption on residues.

A note on invertibility of the Dirac operator twisted with Hilbert-A-module coefficients

Given a closed connected spin manifold M with non-negative and somewhere positive scalar curvature, we show that the Dirac operator twisted with any flat Hilbert module bundle is invertible.

Degree one cohomology with twisted coefficients of the mapping class group

Let $Γ$ be the mapping class group of an oriented surface $Σ$ of genus g with r boundary components. We prove that the first cohomology group $H^1(Γ, O(M_{SL(2, C)})^*)$ is non-trivial, where the coefficient module is the dual of the space of algebraic functions on the $SL(2, C)$ moduli space over $Σ$.

扭曲的Bredon-Illman上同调是Morita不变量

Twisted Bredon-Illman Cohomology is a Morita Invariant

该研究证明Mukherjee-Mukherjee定义的紧李群作用群胚的扭曲Bredon-Illman上同调为Morita不变量，通过双丛转移系数系统推广了普通Bredon-Illman上同调的相关结果，消除了有限迷向条件与系数系统限制。

可定向泊松流形的扭转庞加莱对偶

Twisted Poincaré duality for orientable Poisson manifolds

该论文将扭转泊松模和泊松链复形几何化到泊松流形，证明可定向流形上存在由模向量场诱导的链同构，建立扭转庞加莱对偶，推广了已有对偶定理。