关于de-bar-sub-M II的Poincaré引理的失效

关于某些非欧结构的Poincaré引理

Poincaré's lemma on some non-Euclidean structures

本文证明了$n$维corank 1亚黎曼结构上的Poincaré引理，给出了$\frac{(n-1)n(n^2+3n-2)}{8}$的“卷曲消失”相容性的充分必要条件.特别是，这一结果部分解决了一个公开的问题制定的Calin和张。我们的证明是基于黎曼流形上的Poincaré引理和局部坐标下的Cesàro-Volterra路径积分公式。作为一个副产品，圣维南引理也提供了一般的黎曼流形。在双曲空间和Carnot/Heisenberg群上给出了一些例子。

几何Poincaré引理

Geometric Poincaré Lemma

对微分链的拓扑向量空间建立了Poincaré引理的一个几何形式。特别地，光滑n-流形M的可收缩开子集U中的每个具有紧支撑的微分k-圈是U中具有紧支撑的微分（k+1）-链的边界。应用包括推广的中值定理和罗尔定理。

L_infty，loc -形式的Poincaré引理

Lemma Poincaré for L_infty,loc - forms

证明了R^n上的每个闭L_infty，loc -形式都是正合的.差分是从电流的意义上理解的。证明不使用任何明确的尺规作图法。De Rham定理。

The Poincare lemma, antiexact forms, and fermionic quantum harmonic oscillator

The paper focuses on various properties and applications of the homotopy operator, which occurs in the Poincaré lemma. In the first part, an abstract operator calculus is constructed, where the exterior derivative is an abstract derivative and the homotopy operator plays the role of an abstract integral. This operator calculus can be used to formulate abstract differential equations. An example of the eigenvalue problem that resembles the fermionic quantum harmonic oscillator is presented. The second part presents the dual complex to the Dolbeault bicomplex generated by the homotopy operator o…

An $\mathsf{A}_{\infty}$ version of the Poincaré lemma

We prove a categorified version of the Poincaré lemma. The natural setting for our result is that of $\infty$-local systems. More precisely, we show that any smooth homotopy between maps $f$ and $g$ induces an $\mathsf{A}_\infty$-natural transformation between the corresponding pullback functors. This transformation is explicitly defined in terms of Chen's iterated integrals. In particular, we show that a homotopy equivalence induces a quasi-equivalence on the DG categories of $\infty$-local system.

形式流形的庞加莱引理

Poincaré's lemma for formal manifolds

本文在形式流形与形式李群理论框架下，为系数取形式函数、形式广义函数、紧支撑形式密度或紧支撑形式分布的德拉姆复形建立了庞加莱引理。