According to wikipedia, Topology is concerned with the properties of space that are preserved under continuous deformations, such as stretching and bending, but not tearing or gluing.

It means the cup…is topologically the same as the doughnut… Because we could(hyperthetcially morph, bend and pull either objects) and make the other.

Mug and Torus morph.gif
Public Domain,

How this relates to the project is through comparison. If you can map the comparison topology, which means you have certain rules and parameters that guide a machine to look for specific characterticis(like a human interaction: closeness, timing, body position(facing forward)), then it makes it possible to use relatively simple data to deduce a human interaction…WHO would have thought!

something or other