Betti numbers and stability for configuration spaces via factorization homology
Betti numbers and stability for configuration spaces via factorization homology
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贝蒂数和配置空间的稳定性（通过因式分解同调）
DOI：
10.2140/agt.2017.17.3137
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发表时间：
2014
影响因子：
0.7
通讯作者：
Ben Knudsen
中科院分区：
文献类型：
--
作者：
Ben Knudsen
利用因式分解同调，我们实现了任意流形$M$的无序配置空间的有理同调，可能是由$M$的紧支撑上同调构造的李代数的有理同调。通过在这个李代数的Chvalley-Eilenberg复形中寻找每个构形空间的同调，我们推广了B‘{o}Digheimer-Cohen-Taylor和F’{e}lix-Thomas的定理，并给出了Church和Randal-Williams的同调稳定性结果的一个新的组合证明。我们的方法适用于显式计算，其中包括例子。
Using factorization homology, we realize the rational homology of the unordered configuration spaces of an arbitrary manifold $M$, possibly with boundary, as the homology of a Lie algebra constructed from the compactly supported cohomology of $M$. By locating the homology of each configuration space within the Chevalley-Eilenberg complex of this Lie algebra, we extend theorems of B\"{o}digheimer-Cohen-Taylor and F\'{e}lix-Thomas and give a new, combinatorial proof of the homological stability results of Church and Randal-Williams. Our method lends itself to explicit calculations, examples of which we include.