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A homotopical description of Deligne-Mumford compactifications

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arxiv 2211.05168 v1 pith:G4M2HFXT submitted 2022-11-09 math.AT math.QAmath.SG

Yash Deshmukh This is my paper · ORCID
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We give a description of the Deligne-Mumford properad expressing it as the result of homotopically trivializing S1 families of annuli (with appropriate compatibility conditions) in the properad of smooth Riemann surfaces with parameterized boundaries. This gives an analog of the results of Drummond-Cole and Oancea--Vaintrob in the setting of properads. We also discuss a variation of this trivialization which gives rise to a new partial compactification of Riemann surfaces relevant to the study of operations on symplectic cohomology.

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  1. Calabi-Yau Deformation Quantization

    math.QA 2026-07 conditional novelty 3.0 of 10

    A Calabi-Yau version of Kontsevich's formality morphism is recorded, yielding canonical closed deformation quantizations for unimodular holomorphic Poisson Calabi-Yau manifolds.

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