Configuration Spaces of Graphs with Certain Permitted Collisions
Configuration Spaces of Graphs with Certain Permitted Collisions
复制标题
具有某些允许碰撞的图的配置空间
DOI：
--
复制
发表时间：
2017
影响因子：
0.8
通讯作者：
Eric Ramos
中科院分区：
文献类型：
--
作者：
Eric Ramos
If G is a graph with vertex set V, let Confnsink(G,V)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathrm{Conf}}}_n^{{{\mathrm{sink}}}}(G,V)$$\end{document} be the space of n-tuples of points on G, which are only allowed to overlap on elements of V. We think of Confnsink(G,V)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathrm{Conf}}}_n^{{{\mathrm{sink}}}}(G,V)$$\end{document} as a configuration space of points on G, where points are allowed to collide on vertices. In this paper, we attempt to understand these spaces from two separate, but closely related, perspectives. Using techniques of combinatorial topology we compute the fundamental groups and homology groups of Confnsink(G,V)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathrm{Conf}}}_n^{{{\mathrm{sink}}}}(G,V)$$\end{document} in the case where G is a tree. Next, we use techniques of asymptotic algebra to prove statements about Confnsink(G,V)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathrm{Conf}}}_n^{{{\mathrm{sink}}}}(G,V)$$\end{document}, for general graphs G, whenever n is sufficiently large. It is proven that, for general graphs, the homology groups exhibit generalized representation stability in the sense of Ramos (arXiv:1606.02673, 2016).
If G is a graph with vertex set V, let Confnsink(G,V)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathrm{Conf}}}_n^{{{\mathrm{sink}}}}(G,V)$$\end{document} be the space of n-tuples of points on G, which are only allowed to overlap on elements of V. We think of Confnsink(G,V)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathrm{Conf}}}_n^{{{\mathrm{sink}}}}(G,V)$$\end{document} as a configuration space of points on G, where points are allowed to collide on vertices. In this paper, we attempt to understand these spaces from two separate, but closely related, perspectives. Using techniques of combinatorial topology we compute the fundamental groups and homology groups of Confnsink(G,V)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathrm{Conf}}}_n^{{{\mathrm{sink}}}}(G,V)$$\end{document} in the case where G is a tree. Next, we use techniques of asymptotic algebra to prove statements about Confnsink(G,V)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathrm{Conf}}}_n^{{{\mathrm{sink}}}}(G,V)$$\end{document}, for general graphs G, whenever n is sufficiently large. It is proven that, for general graphs, the homology groups exhibit generalized representation stability in the sense of Ramos (arXiv:1606.02673, 2016).
具有环的树的配置空间的同源性
影响因子：
0.7
作者：
Chettih;Safia;Luetgehetmann;Daniel
通讯作者：
Daniel
DOI：
10.1090/tran/8496
发表时间：
2012-06
期刊：
Forum of Mathematics, Sigma
影响因子：
--
作者：
Steven V. Sam;A. Snowden
通讯作者：
Steven V. Sam;A. Snowden
影响因子：
2
作者：
Jeremy Miller;Jenny Wilson
通讯作者：
Jeremy Miller;Jenny Wilson