  Active nematics contain topological defects which under sufficient activity
move, create and annihilate in a chaotic quasi-steady state, called active
turbulence. However, understanding active defects under confinement is an open
challenge, especially in three-dimensions. Here, we demonstrate the topology of
three-dimensional active nematic turbulence under the spherical confinement,
using numerical modelling. In such spherical droplets, we show the
three-dimensional structure of the topological defects, which due to closed
confinement emerge in the form of closed loops or surface-to-surface spanning
line segments. In the turbulent regime, the defects are shown to be strongly
spatially and time varying, with ongoing transformations between positive
winding, negative winding and twisted profiles, and with defect loops of zero
and non-zero topological charge. The timeline of the active turbulence is
characterised by four types of bulk topology-linked events --- breakup,
annihilation, coalescence and cross-over of the defects --- which we discuss
could be used for the analysis of the active turbulence in different
three-dimensional geometries. The turbulent regime is separated by a first
order structural transition from a low activity regime of a steady-state vortex
structure and an offset single point defect. We also demonstrate coupling of
surface and bulk topological defect dynamics by changing from strong
perpendicular to inplane surface alignment. More generally, this work is aimed
to provide insight into three-dimensional active turbulence, distinctly from
the perspective of the topology of the emergent three-dimensional topological
defects.
