AFFINE BRAID GROUP, JM ELEMENTS AND KNOT HOMOLOGY
AFFINE BRAID GROUP, JM ELEMENTS AND KNOT HOMOLOGY
复制标题
仿射编织群、JM 元素和结同源性
DOI：
10.1007/s00031-018-9478-5
复制
发表时间：
2017
影响因子：
0.7
通讯作者：
L. Rozansky
中科院分区：
文献类型：
--
作者：
A. Oblomkov;L. Rozansky
In this paper we construct a homomorphism of the affine braid group Brnaff\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathfrak{Br}}_n^{\mathrm{aff}} $$\end{document} in the convolution algebra of the equivariant matrix factorizations on the space X¯2=bn×GLn×nn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overline{\mathcal{X}}}_2={\mathfrak{b}}_n\times {\mathrm{GL}}_n\times {\mathfrak{n}}_n $$\end{document} considered in the earlier paper of the authors. We explain that the pull-back on the stable part of the space X¯2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overline{\mathcal{X}}}_2 $$\end{document} intertwines with the natural homomorphism from the affine braid group Brnaff\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathfrak{Br}}_n^{\mathrm{aff}} $$\end{document} to the finite braid group Brn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathfrak{Br}}_n $$\end{document}. This observation allows us derive a relation between the knot homology of the closure of β ∈ Brn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathfrak{Br}}_n $$\end{document} and the knot homology of the closure of β · δ where δ is a product of the JM elements in Brn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathfrak{Br}}_n $$\end{document}
In this paper we construct a homomorphism of the affine braid group Brnaff\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathfrak{Br}}_n^{\mathrm{aff}} $$\end{document} in the convolution algebra of the equivariant matrix factorizations on the space X¯2=bn×GLn×nn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overline{\mathcal{X}}}_2={\mathfrak{b}}_n\times {\mathrm{GL}}_n\times {\mathfrak{n}}_n $$\end{document} considered in the earlier paper of the authors. We explain that the pull-back on the stable part of the space X¯2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overline{\mathcal{X}}}_2 $$\end{document} intertwines with the natural homomorphism from the affine braid group Brnaff\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathfrak{Br}}_n^{\mathrm{aff}} $$\end{document} to the finite braid group Brn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathfrak{Br}}_n $$\end{document}. This observation allows us derive a relation between the knot homology of the closure of β ∈ Brn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathfrak{Br}}_n $$\end{document} and the knot homology of the closure of β · δ where δ is a product of the JM elements in Brn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathfrak{Br}}_n $$\end{document}