The inverse function theorem for curved L-infinity spaces

Autor:	Amorim, Lino, Tu, Junwu
Rok vydání:	2020
Předmět:	Mathematics - Differential Geometry Mathematics - Algebraic Geometry Mathematics - K-Theory and Homology Mathematics - Quantum Algebra
Druh dokumentu:	Working Paper
Popis:	In this paper we prove an inverse function theorem in derived differential geometry. More concretely, we show that a morphism of curved $L_\infty$ spaces which is a quasi-isomorphism at a point has a local homotopy inverse. This theorem simultaneously generalizes the inverse function theorem for smooth manifolds and the Whitehead theorem for $L_\infty$ algebras. The main ingredients are the obstruction theory for $L_\infty$ homomorphisms (in the curved setting) and the homotopy transfer theorem for curved $L_\infty$ algebras. Both techniques work in the $A_\infty$ case as well. Comment: Comments welcome! Title change in the second version. v4: references updated
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2008.01747 Zobrazit plný text záznamu View this record from Arxiv