Multisimplicial chains and configuration spaces

关于配置空间上的coshuffle余乘法

On coshuffle comultiplication on configuration spaces

本文研究了配置空间上的coshuffle余乘法结构，证明其作为DGCoAlg的性质，并探讨了图配置空间的同调原始性分类。

On the cohomology of spaces of links and braids via configuration space integrals

We study the cohomology of spaces of string links and braids in $\mathbb{R}^n$ for $n\geq 3$ using configuration space integrals. For $n>3$, these integrals give a chain map from certain diagram complexes to the deRham algebra of differential forms on these spaces. For $n=3$, they produce all finite type invariants of string links and braids.

正特征下构型空间同调的点集构造

Homology of configuration spaces in positive characteristic via point-set constructions

本文通过显式链复形计算正特征下流形（无序）构型空间的同调，将Knudsen定理提升至模型范畴层次，并构造新的谱序列收敛到这些同调群。