# Manchester Geometry Seminar 2014/2015

**Thursday 27 November 2014. ** *The Frank Adams Room (Room 1.212), the Alan Turing Building. 4.15pm*
##
The Geometrisation of Degree $2$ $N$-Manifolds, and of Lie $2$-Algebroids

Madeleine Jotz Lean (University of Sheffield)

`m.jotz-lean@sheffield.ac.uk`

I will sketch how $N$-manifolds of degree $2$ are equivalent to
double vector bundles endowed with a linear metric. Then I will
explain the correspondence of VB-Courant algebroids with
Lie $2$-algebroids. In order to do this, I will define the notion of Dorfman
2-representation, the "dual" of a Lie $2$-algebroid.
I will then describe how this correspondence gives rise to several new classes of
examples of Lie $2$-algebroids, such as the bicrossproducts of representations up to homotopy.