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Formality of a higher-codimensional Swiss-cheese operad

Najib Idrissi

Algebraic & Geometric Topology 22 (2022) 55–111
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 2. We define a higher-codimensional variant of the Swiss-cheese operad, called the complementarily constrained disks operad CDmn, associated to such configurations. The operad CDmn is weakly equivalent to the operad of locally constant factorization algebras on the stratified space {m n}. We prove that this operad is formal over .

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