Engel群上的谱复形与流
Spectral complexes and currents on the Engel group
- Department of Pure Mathematics, University of Leeds（利兹大学纯数学系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究Engel群上de Rham复形产生的谱复形，描述其结构、紧支撑版本及对偶谱流，证明光滑谱复形嵌入流复形，并给出Pansu拉回诱导态射的条件。
AI中文摘要：
我们研究了将Engel群$G$视为截断多重复形时，由de Rham复形产生的谱复形。我们描述了所得的两个复形，分析了其紧支撑对应物，并通过对偶定义了相应的谱流。我们证明了光滑谱复形自然嵌入到流复形中。最后，我们证明了当$q>7$时，$W_{\mathrm{loc}}^{1,q}$映射$\varphi\colon G\to G$的Pansu拉回诱导出相应谱流复形间的态射。
英文摘要：
We study the spectral complexes arising from the de Rham complex on the Engel group $G$ viewed as a truncated multicomplex. We describe the two resulting complexes, analyse their compactly supported counterparts, and define the corresponding spectral currents by duality. We prove that the smooth spectral complexes embed naturally into the current complexes. Finally, we show that the Pansu pullback of a $W_{\mathrm{loc}}^{1,q}$ map $φ\colon G\to G$ with $q>7$ induces a morphism into the corresponding complexes of spectral currents.
