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Kaledin classes and formality criteria

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arxiv 2404.17529 v1 pith:2YOHQQHT submitted 2024-04-26 math.AT math.AGmath.QA

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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Simplicial properadic homotopy

    math.AT 2025-05 conditional novelty 7.0 of 10

    A simplicial category of homotopy gebras over properads is constructed, and infinity-quasi-isomorphisms are shown to coincide with zig-zags of quasi-isomorphisms.

  2. Obstruction sequences to homotopy equivalences

    math.AT 2025-09 conditional novelty 6.0 of 10

    Gauge-theoretic obstruction sequences characterize homotopy equivalences between algebras over properads and colored operads, with applications to minimal models over general fields and in etale cohomology.

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