Models for configuration spaces of points via obstruction theory I

TL;DR

This paper develops algebraic models for configuration spaces of points on manifolds using obstruction theory, avoiding traditional geometric or analytic methods.

Contribution

It introduces a purely algebraic approach to modeling configuration spaces through Sullivan models derived from obstruction theory.

Findings

Provides rational models for configuration spaces

Uses algebraic obstruction theory instead of geometric methods

Simplifies the derivation of models for configuration spaces

Abstract

We derive rational (Sullivan) models for configuration spaces of points on manifolds purely from algebraic considerations via obstruction theory, essentially without the use of analytic or geometric techniques.