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L-infinity spaces and derived loop spaces

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arxiv 1404.5426 v3 pith:MCDORQUS submitted 2014-04-22 math.AG math.DGmath.QA

Ryan Grady , Owen Gwilliam This is my paper · ORCID
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keywords spacesderivedl-infinitycostellofieldlooptheoryapproach
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We develop further the approach to derived differential geometry introduced in Costello's work on the Witten genus. In particular, we introduce several new examples of L-infinity spaces, discuss vector bundles and shifted symplectic structures on L-infinity spaces, and examine in some detail the example of derived loop spaces. This paper is background for a companion paper, in which we define a quantum field theory on a derived stack, building upon Costello's definition of an effective field theory.

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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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