TY - JOUR
T1 - Differential Graded Manifolds of Finite Positive Amplitude
AU - Behrend, Kai
AU - Liao, Hsuan Yi
AU - Xu, Ping
N1 - Publisher Copyright:
© The Author(s) 2024. Published by Oxford University Press.
PY - 2024/4/1
Y1 - 2024/4/1
N2 - 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.
AB - 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.
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U2 - 10.1093/imrn/rnae023
DO - 10.1093/imrn/rnae023
M3 - Article
AN - SCOPUS:85189526179
SN - 1073-7928
VL - 2024
SP - 7160
EP - 7200
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 8
ER -