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Article Dans Une Revue J.Reine Angew.Math. Année : 2024

Deformation theory of Cohomological Field Theories

Résumé

We develop the deformation theory of cohomological field theories (CohFTs), which is done as a special case of a general deformation theory of morphisms of modular operads. This leads us to introduce two new natural extensions of the notion of a CohFT: homotopical (necessary to structure chain-level Gromov--Witten invariants) and quantum (with examples found in the works of Buryak--Rossi on integrable systems). We introduce a new version of Kontsevich's graph complex, enriched with tautological classes on the moduli spaces of stable curves. We use it to study a new universal deformation group which acts naturally on the moduli spaces of quantum homotopy CohFTs, by methods due to Merkulov--Willwacher. This group is shown to contain both the prounipotent Grothendieck--Teichmüller group and the Givental group.

Dates et versions

hal-02870850 , version 1 (16-06-2020)

Identifiants

Citer

Vladimir Dotsenko, Sergey Shadrin, Arkady Vaintrob, Bruno Vallette. Deformation theory of Cohomological Field Theories. J.Reine Angew.Math., 2024, 2024 (809), pp.91-157. ⟨10.1515/crelle-2023-0098⟩. ⟨hal-02870850⟩
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