Derived Manifolds as Differential Graded Manifolds
Differential Geometry
2023-03-21 v1 Algebraic Geometry
Algebraic Topology
Abstract
On one hand, together with Pelle Steffens, we recently characterized the infinity category of derived manifolds up to equivalence by a universal property. On the other hand, it is shown in recent work of Behrend-Liao-Xu that the category of differential graded manifolds admits a homotopy theory. In this paper, we prove that the associated infinity category of dg-manifolds is equivalent to that of derived manifolds. This allows the well developed theory of dg-geometry to live in symbiosis with infinity categorical approach to derived differential geometry. As a consequence, we prove that a dg-C-infinity-algebra is homotopically finitely presented if and only if it is quasi-isomorphic to smooth functions on a dg-manifold.
Cite
@article{arxiv.2303.11140,
title = {Derived Manifolds as Differential Graded Manifolds},
author = {David Carchedi},
journal= {arXiv preprint arXiv:2303.11140},
year = {2023}
}