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} }
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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