Pretty rational models for Poincar\'e duality pairs

TL;DR

This paper establishes that many Poincaré duality pairs can be modeled rationally using Sullivan models, facilitating the study of configuration spaces in manifolds with boundary.

Contribution

It introduces a class of rational models for Poincaré duality pairs, enhancing the understanding of their algebraic structure and applications.

Findings

Existence of rational models for a large class of Poincaré duality pairs

Construction of Sullivan models with a special form

Applications to configuration spaces in manifolds with boundary

Abstract

We prove that a large class of Poincar\'e duality pairs admit rational models (in the sense of Sullivan) of a particularly nice form associated to some Poincar\'e duality CDGA. These models have applications in particular to the construction of rational models of configuration spaces in compact manifolds with boundary.