  In this paper we prove a toric localization formula in cohomological
Donaldson Thomas theory. Consider a -1-shifted symplectic algebraic space with
a C* action leaving the -1-shifted symplectic form invariant. This includes the
moduli space of stable sheaves or complexes of sheaves on a Calabi-Yau
threefold with a C*-invariant Calabi-Yau form, or the intersection of two
C*-invariant Lagrangians in a symplectic space with a C*-invariant symplectic
form. In this case we express the restriction of the Donaldson-Thomas perverse
sheaf (or monodromic mixed Hodge module) defined by Joyce et al. to the
attracting variety as a sum of cohomological shifts of the DT perverse sheaves
on the C* fixed components. This result can be seen as a -1-shifted version of
the Bialynicki-Birula decomposition for smooth schemes.
