Work

Kaledin classes and formality criteria

Year: 2026

Type: article

Abstract: We develop a general obstruction theory to the formality of algebraic structures over any commutative ground ring. It relies on the construction of Kaledin obstruction classes that faithfully detect the formality of differential graded algebras over operads or properads, possibly colored in groupoids. The present treatment generalizes the previous obstruction classes in two directions: outside characteristic zero and including a wider range of algebraic structures. This enables us to establish novel formality criteria, including formality descent with torsion coefficients, formality in families, intrinsic formality, and criteria in terms of chain-level lifts of homology automorphism.

Source: Advances in Mathematics

DOI: 10.1016/j.aim.2026.111376

Author: Coline Emprin

Institutions: Stockholm University, Université Paris Sciences et Lettres, École Normale Supérieure - PSL, Laboratoire Analyse, Géométrie et Applications, Département de mathématiques et applications

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,790

Funders: École Normale Supérieure, Agence Nationale de la Recherche, Université Paris 13