Discrete) Morse Theory on Configuration Spaces
Discrete) Morse Theory on Configuration Spaces
复制标题
配置空间的离散）莫尔斯理论
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
M. Salvetti
中科院分区：
文献类型：
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作者：
Francesca Mori;M. Salvetti
R中的经典配置空间(有时记为F(n，R))定义为R中不同点成对的n个有序−元组的集合，取坐标(R)=Rxij，i=1，.。。，n，j=1，.。。，d有F(n，R)=R∪i6=jHij，其中Hij是余维d子空间∩k=1，…，d{xik=xjk}。因此，后一个子空间是R中d个超平面的交集，每个超平面由超平面hij={x∈R：xi=xj}获得，考虑(R)=R的第k个−分量，k=1，.。。广义配置空间(简称为配置空间)指的是从R中的任何超平面排列A开始的模拟构造，对于每个d>；0，都有A的d-−复合化A⊂R，它由d-复合化子空间的集合{H，H∈A}给出。与A相关联的配置空间是子空间排列的补充
Classical Configuration Spaces in R (sometimes written as F (n, R)) are defined as the set of ordered n−tuples of pairwise different points in R. Taking coordinates in (R) = R xij , i = 1, . . . , n, j = 1, . . . , d, one has F (n, R) = R ∪i 6=j H ij , where H ij is the codimension-d subspace ∩k=1,...,d {xik = xjk}. So, the latter subspace is the intersection of d hyperplanes in R, each obtained by the hyperplane Hij = {x ∈ R : xi = xj}, considered on the k−th component in (R) = R, k = 1, . . . , d. By a Generalized Configuration Space (for brevity, simply a Configuration Space) we mean an analog construction, which starts from any Hyperplane Arrangement A in R. For each d > 0, one has a d−complexification A ⊂ R of A, which is given by the collection {H, H ∈ A} of the d-complexified subspaces. The configuration space associated to A is the complement to the subspace arrangement