  The use of standard rulers, such as the scale of the Baryonic Acoustic
oscillations (BAO), has become one of the more powerful techniques employed in
cosmology to probe the entity driving the accelerating expansion of the
Universe. In this paper, the topology of large scale structure (LSS) is used as
one such standard ruler to study this mysterious `dark energy'. By following
the redshift evolution of the clustering of luminous red galaxies (LRGs) as
measured by their 3D topology (counting structures in the cosmic web), we can
chart the expansion rate and extract information about the equation of state of
dark energy. Using the technique first introduced in (Park & Kim, 2009), we
evaluate the constraints that can be achieved using 3D topology measurements
from next-generation LSS surveys such as the Baryonic Oscillation Spectroscopic
Survey (BOSS). In conjunction with the information that will be available from
the Planck satellite, we find a single topology measurement on 3 different
scales is capable of constraining a single dark energy parameter to within 5%
and 10% when dynamics are permitted. This offers an alternative use of the data
available from redshift surveys and serves as a cross-check for BAO studies.
