Towards an sl2 action on the annular Khovanov spectrum
Towards an sl2 action on the annular Khovanov spectrum
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环形 Khovanov 谱上的 sl2 作用
DOI：
10.1016/j.aim.2022.108581
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发表时间：
2022
影响因子：
1.7
通讯作者：
Willis, Michael
中科院分区：
文献类型：
--
作者：
Akhmechet, Rostislav;Krushkal, Vyacheslav;Willis, Michael
给定加厚环上的一个连杆，它的环Khovanov同调带有李代数sl 2的作用，这对于环连杆协配是自然的。我们考虑将这一作用提升到环同伦的稳定同伦细化的问题。作为该计划的一部分，sl 2的标准发生器的作用被提升到光谱图。特别地，可以得出sl对同调的作用与Steenrod代数的作用可以交换。本文开发的主要新技术成分可能是独立的兴趣，涉及分辨率立方体中的某些类型的消去以及由此产生的框架流类中模空间的更复杂结构。
Given a link in the thickened annulus, its annular Khovanov homology carries an action of the Lie algebra 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 sl 2 are lifted to maps of spectra. In particular, it follows that the 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.