Quantum link homology via trace functor I

• 成果类型: Article
• 署名作者: Beliakova, Anna; Putyra, Krzysztof K.; Wehrli, Stephan M.
• 署名单位: University of Zurich; Syracuse University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-018-0830-0
• 发表日期: 2019
• 页码: 383-492
• 关键词: highest weight categories; khovanov homology; tangle

摘要

Motivated by topology, we develop a general theory of traces and shadows for an endobicategory, which is a pair: bicategory and endobifunctor . For a graded linear bicategory and a fixed invertible parameter q, we quantize this theory by using the endofunctor sigma q such that sigma q:=q-deg sigma for any 2-morphism and coincides with sigma otherwise. Applying the quantized trace to the bicategory of Chen-Khovanov bimodules we get a new triply graded link homology theory called quantum annular link homology. If q=1 we reproduce Asaeda-Przytycki-Sikora homology for links in athickened annulus. We prove that our homology carries an action of , which intertwines the action of cobordisms. In particular, thequantum annular homology of an n-cable admits an action of the braid group, which commutes with thequantum group action and factors through theJones skein relation. This produces anontrivial invariant for surfaces knotted in four dimensions. Moreover, adirect computation for torus links shows that therank of quantum annular homology groups depend on thequantum parameter q.