Diffeomorphisms of discs

TL;DR

This paper reviews current knowledge on the rational homotopy type of diffeomorphism groups of discs and related homeomorphism groups in dimensions five and higher.

Contribution

It summarizes the known results regarding the rational homotopy types of these groups for dimensions d ≥ 5.

Findings

Current understanding of the rational homotopy type for diffeomorphism groups in high dimensions

Connections between diffeomorphisms of discs and Euclidean space homeomorphisms

Summary of known results in the field

Abstract

I describe what is currently known, for $d \geq 5$, about the rational homotopy type of the group of diffeomorphisms of the $d$-disc relative to its boundary, and the closely related group of homeomorphisms of $d$-dimensional Euclidean space.