Higher-categorical combinatorics of configuration spaces of Euclidean space

TL;DR

This paper explores the homotopy types of configuration spaces in Euclidean spaces using higher category theory and stratified spaces, providing a new categorical perspective on classical topological problems.

Contribution

It introduces a higher categorical framework to analyze configuration spaces of Euclidean space, connecting stratified spaces with $ extbf{ extTheta}_n$ categories for the first time.

Findings

Homotopy types characterized via $ extbf{ extTheta}_n$ categories

Higher categorical methods clarify configuration space structures

New connections between stratified spaces and homotopy theory

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 $\mathbf{\Theta}_n$.