Pré-Publication, Document De Travail Année : 2024

Algebras over not too little discs

Résumé

By the introduction of locally constant prefactorization algebras at a fixed scale, we show a mathematical incarnation of the fact that observables at a given scale of a topological field theory propagate to every scale over euclidean spaces. The key is that these prefactorization algebras over ℝ n are equivalent to algebras over the little n-disc operad. For topological field theories with defects, we get analogous results by replacing ℝ n with the spaces modelling corners ℝ p × ℝ q ≥0 . As a toy example in 1d, we quantize, once more, constant Poisson structures.

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Dates et versions

hal-04924526 , version 1 (31-01-2025)
hal-04924526 , version 2 (03-02-2026)

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Damien Calaque, Victor Carmona. Algebras over not too little discs. 2024. ⟨hal-04924526v1⟩
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