# Deformation theory of Cohomological Field Theories

@article{Dotsenko2020DeformationTO, title={Deformation theory of Cohomological Field Theories}, author={Vladimir Dotsenko and Sergey Shadrin and Arkady Vaintrob and Bruno Vallette}, journal={arXiv: Algebraic Geometry}, year={2020} }

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…

## 7 Citations

### MODULAR NORI MOTIVES

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In a previous article [CMMar20], we developed the pioneering Grothendieck approach to the problem of description of the absolute Galois group Gal(Q/Q) based upon dessins d’enfant. Namely, we replaced…

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These notes represent the transcript of three, 90 minute lectures given by the second author at the CRM in Barcelona in 2021 as part of the"Higher Structures and Operadic Calculus"workshop. The goal…

### Toward a minimal model for $H_\ast(\overline{\mathcal{M}})$.

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- 2020

The modular operad $H_\ast(\overline{\mathcal{M}}_{g,n})$ of the homology of Deligne-Mumford compactifications of moduli spaces of pointed Riemann surfaces has a minimal model governed by higher…

### Massey Products for Graph Homology

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### Reconnectads

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- 2022

A BSTRACT . We introducea new operad-like structurethat we call a reconnectad; the “input” of an element of a reconnectad is a ﬁnite simple graph, rather than a ﬁnite set

### Toward a minimal model for H∗(M¯)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_*(\overline{\mathcal {M}})$$\end{do

- Materials ScienceJournal of Homotopy and Related Structures
- 2022

The modular operad H∗(M¯g,n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…

### Modular operads as modules over the Brauer properad

- Mathematics
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We show that modular operads are equivalent to modules over a certain simple properad which we call the Brauer properad. Furthermore we show that, in this setting, the Feynman transform corresponds…

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