欧氏空间构型空间的高阶范畴组合学

Anna Cepek

欧氏空间构型空间的高阶范畴组合学

代数拓扑 2024-09-02 v4

作者: Anna Cepek

在 arXiv 上查看 ↗ PDF ↗

摘要

我们通过分层空间，在 $\infty$ -范畴的同伦论语境中考察流形的有限子集的构型。借助这些高阶范畴方法，就 n 维欧氏空间的情形，我们根据范畴 $\mathbf{\Theta}_n$ 辨识出此类构型空间的商伦类型。

关键词

构型空间欧氏空间 $\infty$-范畴分层空间同伦类型 $\mathbf{\Theta}_n$ 范畴

引用

@article{arxiv.1910.11980,
  title  = {Higher-categorical combinatorics of configuration spaces of Euclidean space},
  author = {Anna Cepek},
  journal= {arXiv preprint arXiv:1910.11980},
  year   = {2024}
}

备注

Reorganized the paper mainly by including an appendix reviewing stratified spaces, exit-path $\infty$-categories, and the theta-n categories; added motivation/contex for main definitions as numerous remarks, mainly in the appendix; corrected Obs. 2.0.11 (previously Obs. 8.0.8), and changed the introduction to include a discussion on trees early on

欧氏空间构型空间的高阶范畴组合学

摘要

关键词

引用

备注

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