  We investigate the structure of smooth and horizonless microstate geometries
in six dimensions, in the spirit of the five-dimensional analysis of Gibbons
and Warner [arXiv:1305.0957]. In six dimensions, which is the natural setting
for horizonless geometries with the charges of the D1-D5-P black hole, the
natural black objects are strings and there are no Chern-Simons terms for the
tensor gauge fields. However, we still find that the same reasoning applies: in
absence of horizons, there can be no smooth stationary solutions without
non-trivial topology. We use topological arguments to describe the Smarr
formula in various examples: the uplift of the five-dimensional minimal
supergravity microstates to six dimensions, the two-charge D1-D5 microstates,
and the non-extremal JMaRT solution. We also discuss D1-D5-P superstrata and
confirm that the Smarr formula gives the same result as for the D1-D5
supertubes which are topologically equivalent.
