The inverse function theorem for curved -infinity spaces

  • Lino Amorim

    Kansas State University, Manhattan, USA
  • Junwu Tu

    ShanghaiTech University, China
The inverse function theorem for curved $L$-infinity spaces cover
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In this paper, we prove an inverse function theorem in derived differential geometry. More concretely, we show that a morphism of curved 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 algebras. The main ingredients are the obstruction theory for homomorphisms (in the curved setting) and the homotopy transfer theorem for curved algebras. Both techniques work in the case as well.

Cite this article

Lino Amorim, Junwu Tu, The inverse function theorem for curved -infinity spaces. J. Noncommut. Geom. 16 (2022), no. 4, pp. 1445–1477

DOI 10.4171/JNCG/484