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arXiv · 1505.03698

The curvature problem for formal and infinitesimal deformations

Wendy Lowen·Michel Van den Bergh
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Abstract

We interpret all Maurer-Cartan elements in the formal Hochschild complex of a small dg category which is cohomologically bounded above in terms of torsion Morita deformations. This solves the "curvature problem", i.e. the phenomenon that such Maurer-Cartan elements naturally parameterize curved A_infinity deformations. In the infinitesimal setup, we show how (n+1)-th order curved deformations give rise to n-th order uncurved Morita deformations.

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Wendy Lowen, Michel Van den Bergh. 2015-05-14. The curvature problem for formal and infinitesimal deformations. https://arxiv.org/abs/1505.03698

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