  We derive a hydrodynamic description of metric-free active matter: starting
from self-propelled particles aligning with neighbors defined by "topological"
rules, not metric zones, -a situation advocated recently to be relevant for
bird flocks, fish schools, and crowds- we use a kinetic approach to obtain
well-controlled nonlinear field equations. We show that the density-independent
collision rate per particle characteristic of topological interactions
suppresses the linear instability of the homogeneous ordered phase and the
nonlinear density segregation generically present near threshold in metric
models, in agreement with microscopic simulations.
