Advances in Mathematics· 2026Q1
Kaledin classes and formality criteria
- 12citations
- Q1SCImago
- 2026year
Short summary
A new obstruction theory using Kaledin classes is developed to detect the formality of differential graded algebras over operads/properads, generalizing previous methods to non-characteristic zero and wider algebraic structures.
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Key points
- Developed Kaledin obstruction classes for a general obstruction theory to formality.
- Detects formality of differential graded algebras over operads or properads.
- Generalizes previous obstruction classes to non-characteristic zero and wider algebraic structures.
- Establishes novel formality criteria including formality descent with torsion and formality in families.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Advances in Mathematics, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics