Formality of little disks and algebraic geometry

TL;DR

This paper constructs a canonical chain of formality quasi-isomorphisms linking the operads of chains on framed and unframed little disks using logarithmic algebraic geometry, with a focus on rational and integral definability.

Contribution

It introduces a novel rational and integral approach to formality quasi-isomorphisms for little disks operads via logarithmic algebraic geometry.

Findings

Constructed a canonical chain of formality quasi-isomorphisms

Achieved rational and integral definability in de Rham cohomology

Applied logarithmic algebraic geometry to operad formality

Abstract

We construct a canonical chain of formality quasiisomorphisms for the operad of chains on framed little disks and the operad of chains on little disks. The construction is done in terms of logarithmic algebraic geometry and is remarkable for being rational (and indeed definable integrally) in de Rham cohomology.