Subdivisional Spaces and Graph Braid Groups
Subdivisional Spaces and Graph Braid Groups
复制标题
细分空间和图形编织组
作者：
B. An;Gabriel C. Drummond;Ben Knudsen
研究了有限胞腔复形X的位形空间的同调计算问题。我们继续观察X$，连同它的细分，作为一个细分空间-一种细胞复合体类别中的图表对象。在发展了一个版本的莫尔斯理论的子空间，我们分解$X$和显示的同源性的配置空间的$X$的计算由导出的张量积的莫尔斯复的分解，一个类似的monoidal切除性质的因式分解同源性。
将这一理论应用到图的构型空间中，我们恢复了由于Escherwietkowski的胞腔链模型。我们的方法来推导这个模型增强了它与各种方便的功能，确切的序列，和模块结构，我们利用在众多的计算，旧的和新的。
We study the problem of computing the homology of the configuration spaces of a finite cell complex $X$. We proceed by viewing $X$, together with its subdivisions, as a subdivisional space--a kind of diagram object in a category of cell complexes. After developing a version of Morse theory for subdivisional spaces, we decompose $X$ and show that the homology of the configuration spaces of $X$ is computed by the derived tensor product of the Morse complexes of the pieces of the decomposition, an analogue of the monoidal excision property of factorization homology.
Applying this theory to the configuration spaces of a graph, we recover a cellular chain model due to Świątkowski. Our method of deriving this model enhances it with various convenient functorialities, exact sequences, and module structures, which we exploit in numerous computations, old and new.
图编织群同源性中的边缘稳定性
影响因子：
2
作者：
An, Byung Hee;Drummond-Cole, Gabriel;Knudsen, Ben
通讯作者：
Knudsen, Ben