  We show that relativistic rotation transformations represent transfer maps
between the laboratory system and a local observer on an observer manifold,
rather than an event manifold, in the spirit of C-equivalence. Rotation is,
therefore, not a parameterised motion on a background space or spacetime, but
is determined by a particular sequence of tetrads related by specific special
Lorentz transformations or boosts. Because such Lorentz boosts do not form a
group, these tetrads represent distinct observers that cannot put together
their local descriptions into a manifold in the usual sense. The choice of
observer manifold depends on the dynamical situation under consideration, and
is not solely determined by the kinematics. Three examples are given:
Franklin's rotation transformation for uniform plane rotation, the Thomas
precession of a vector attached to an electron, and the motion of a charged
particle in an electromagnetic field. In each case, at each point of its
trajectory, there is a distinguished tetrad and a special Lorentz
transformation that maps Minkowski space to the spacetime of the local observer
on the curve.
