# Graded Geometry, Q‐Manifolds, and Microformal Geometry

@article{Voronov2019GradedGQ,
title={Graded Geometry, Q‐Manifolds, and Microformal Geometry},
author={Theodore Th. Voronov},
journal={Fortschritte der Physik},
year={2019},
volume={67}
}
• T. Voronov
• Published 7 March 2019
• Mathematics
• Fortschritte der Physik
We give an exposition of graded and microformal geometry, and the language of Q‐manifolds. Q‐manifolds are supermanifolds endowed with an odd vector field of square zero. They can be seen as a non‐linear analogue of Lie algebras (in parallel with even and odd Poisson manifolds), a basis of “non‐linear homological algebra”, and a powerful tool for describing algebraic and geometric structures. This language goes together with that of graded manifolds, which are supermanifolds with an extra Z…
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