# Linear generalised complex structures

#### 08.01.2021, 11:00  –  Online Meeting Arbeitsgruppenseminar Analysis

Malte Heuer (University of Hamburg)

Generalised complex structures were introduced by Nigel Hitchin and studied by Marco Gualtieri as a unification of complex and symplectic structures. In this talk I will first recall basic definitions in generalised geometry and then introduce linear generalised complex structures on vector bundles. We will see that these are a natural generalisation of holomorphic vector bundles and how they can be studied via adapted linear splittings and Dorfman connections. We show an equivalence between linear generalised complex structures on a vector bundle $E$ and certain complex Lie algebroid structures on $TM\oplus E^*$. The talk is based on joint work with Madeleine Jotz Lean.

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