  Topological phases which host Majorana fermions can not be identified via
local order parameters. We give simple nonlocal order parameters to distinguish
quasi-one-dimensional (1D) topological superconductors of spinless fermions,
for any interacting model in the absence of time reversal symmetry. These
string or "brane" order parameters are natural for measurements in cold atom
systems using quantum gas microscopy. We propose them as a way to identify
symmetry-protected topological phases of Majorana fermions in cold atom
experiments via bulk rather than edge degrees of freedom. Subsequently, we
study two-dimensional (2D) topological superconductors via the quasi-1D limit
of coupling $N$ identical chains on the cylinder. We classify the symmetric,
interacting topological phases protected by the additional $\mathbb{Z}_N$
translation symmetry. The phases include quasi-1D analogs of (i) the $p+ip$
chiral topological superconductor, which can be distinguished up to the 2D
Chern number mod 2, and (ii) the 2D weak topological superconductor. We devise
general rules for constructing nonlocal order parameters which distinguish the
phases. These rules encode the signature of the fermionic topological phase in
the symmetry properties of the terminating operators of the nonlocal string or
brane. The nonlocal order parameters for some of these phases simply involve a
product of the string order parameters for the individual chains. Finally, we
give a physical picture of one of the topological phases as a condensate of
certain defects, which motivates the form of the nonlocal order parameter and
is reminiscent of higher dimensional constructions of topological phases.
