Differential Graded Manifolds of Finite Positive Amplitude

Kai Behrend, Hsuan Yi Liao, Ping Xu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We prove that dg manifolds of finite positive amplitude, that is, bundles of positively graded curved L∞[1]-algebras, form a category of fibrant objects. As a main step in the proof, we obtain a factorization theorem using path spaces. First we construct an infinite-dimensional factorization of a diagonal morphism using actual path spaces motivated by the AKSZ construction. Then we cut down to finite dimensions using the Fiorenza-Manetti method. The main ingredient in our method is the homotopy transfer theorem for curved L∞[1]-algebras. As an application, we study the derived intersections of manifolds.

Original languageEnglish (US)
Pages (from-to)7160-7200
Number of pages41
JournalInternational Mathematics Research Notices
Volume2024
Issue number8
DOIs
StatePublished - Apr 1 2024

All Science Journal Classification (ASJC) codes

  • General Mathematics

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