Lie algebroid Fibrations

Understand

A degree 1 non-negative graded super manifold equipped with a degree 1 vector field Q satisfying [Q, Q]=1, namely a so-called NQ-1 manifold is, in plain differential geometry language, a Lie algebroid.

• We introduce a notion of fibration for such super manifols, that essentially involves a complete Ehresmann connection.
• As it is the case for Lie algebras, such fibrations turn out not to be just locally trivial products.
• We also define homotopy groups and prove the expected long exact sequence associated to a fibration.