论文标题
迈向$ \ mathfrak {sl} _2 $ Annular Khovanov Spectrum spectrum
Towards an $\mathfrak{sl}_2$ action on the annular Khovanov spectrum
论文作者
论文摘要
鉴于浓稠的环中的链接，其环形khovanov同源性具有Lie代数$ \ Mathfrak {SL} _2 $的作用，这对于环形链路cobordism是很自然的。我们考虑将这一动作提升为环形同源性稳定同质性改进的问题。作为该程序的一部分，将$ \ mathfrak {sl} _2 $的标准发电机的动作提升为光谱地图。特别是，因此，$ \ mathfrak {sl} _2 $同源性动作通过steenrod代数的动作进行通勤。本文中开发的主要新技术成分可能具有独立的兴趣，它涉及分辨率立方中某些类型的取消，以及在框架流量类别中产生的模量空间的更复杂的结构。
Given a link in the thickened annulus, its annular Khovanov homology carries an action of the Lie algebra $\mathfrak{sl}_2$, which is natural with respect to annular link cobordisms. We consider the problem of lifting this action to the stable homotopy refinement of the annular homology. As part of this program, the actions of the standard generators of $\mathfrak{sl}_2$ are lifted to maps of spectra. In particular, it follows that the $\mathfrak{sl}_2$ action on homology commutes with the action of the Steenrod algebra. The main new technical ingredients developed in this paper, which may be of independent interest, concern certain types of cancellations in the cube of resolutions and the resulting more intricate structure of the moduli spaces in the framed flow category.
