Modular classes of \(Q\)-manifolds: a review and some applications. (English) Zbl 1424.53114

Bruce, Andrew James

Arch. Math., Brno 53, No. 4, 203-219 (2017).

This paper reviews the modular class of a \(Q\)-manifold and applies it to several examples. Let us recall that the notion of the modular class was first introduced by Koszul and then reintroduced by Weinstein, but it is not well known. This modular class is interpreted as the obstruction to the existence of a \(Q\)-invariant Berezin volume. The author studies also \(L_{\infty}\)-algebroids and higher Poisson manifolds.

Reviewer: Angela Gammella-Mathieu (Metz)

MSC:

53D17	Poisson manifolds; Poisson groupoids and algebroids
17B66	Lie algebras of vector fields and related (super) algebras
57R20	Characteristic classes and numbers in differential topology
58A50	Supermanifolds and graded manifolds

Keywords:

\(Q\)-manifold; supermanifold; Berezin volume; Poisson manifolds; higher Poisson manifolds; modular classes; \(L_{\infty}\)-algebroids