  A methodology is proposed for inferring the topology underlying point cloud
data. The approach employs basic elements of Morse Theory, and is capable of
producing not only a point estimate of various topological quantities (e.g.,
genus), but it can also assess their sampling uncertainty in a probabilistic
fashion. Several examples of point cloud data in three dimensions are utilized
to demonstrate how the method yields interval estimates for the topology of the
data as a 2-dimensional surface embedded in R^3.
