English

Higher-categorical combinatorics of configuration spaces of Euclidean space

Algebraic Topology 2024-09-02 v4

Abstract

We examine configurations of finite subsets of manifolds within the homotopy-theoretic context of \infty-categories by way of stratified spaces. Through these higher categorical means, we identify the homotopy types of such configuration spaces in the case of n-dimensional Euclidean space in terms of the category Θn\mathbf{\Theta}_n.

Keywords

Cite

@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}
}

Comments

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