Formality of a higher-codimensional Swiss-cheese operad

Idrissi, Najib

doi:10.2140/agt.2022.22.55

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Formality of a higher-codimensional Swiss-cheese operad

Najib Idrissi

Algebraic & Geometric Topology 22 (2022) 55–111

DOI: 10.2140/agt.2022.22.55

Abstract

We study bicolored configurations of points in the Euclidean $n$ –space that are constrained to remain either inside or outside a fixed Euclidean $m$ –subspace, with $n - m \geq 2$ . We define a higher-codimensional variant of the Swiss-cheese operad, called the complementarily constrained disks operad ${C D}_{m n}$ , associated to such configurations. The operad ${C D}_{m n}$ is weakly equivalent to the operad of locally constant factorization algebras on the stratified space ${ℝ^{m} \subset ℝ^{n}}$ . We prove that this operad is formal over $ℝ$ .

Keywords

Fulton–MacPherson compactification, graph complexes, constrained little disks, semialgebraic forms, relative loop spaces

Mathematical Subject Classification 2010

Primary: 18D50, 55P48

Secondary: 55R80

References

Publication

Received: 23 January 2019

Revised: 23 October 2020

Accepted: 8 December 2020

Published: 26 April 2022

Authors

Najib Idrissi
IMJ-PRG CNRS Université de Paris and Sorbonne Université Paris France

Volume 22, issue 1 (2022)