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Non-commutative formality implies commutative and Lie formality

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arxiv 1609.02540 v2 pith:7FGBJ3KW submitted 2016-09-08 math.AT math.KTmath.QA

Bashar Saleh This is my paper · ORCID
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Over a field of characteristic zero we prove two formality conditions. We prove that a dg Lie algebra is formal if and only if its universal enveloping algebra is formal. We also prove that a commutative dg algebra is formal as a dg associative algebra if and only if it is formal as a commutative dg algebra. We present some consequences of these theorems in rational homotopy theory.

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  1. 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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