I've been reading a lot about Hi-C lately, and this has been bothering me. So far as I can tell from reading around, the topology is related to the conformation of the linear chromosome. This seems like a fairly pointless description however, as they should all have the same topology. A "conformation", in my understanding, is the chromosome being folded into a particular geometry.
On the other hand though, I guess if two genes were brought together to form a loop, they would also form a "hole" (the gap in the loop). But this seems like a weak connection to make, just because two chromosome regions are paired doesn't necessarily mean they were bound and formed a loop. It seems the "topology" would "best" be seen after a 3D reconstruction from the pairs data, showing the predicted geometry, and from there you could see how many putative loops and such there are, and thus start to determine the topological properties.
The last possibility I was thinking was that this is in reference to network topology implied by a contact matrix. This seems the most likely to me, but also the least implied (to me, at least) in the literature I've ever read.
All of this has me wondering if I've missed something about the meaning of "topology" here, as opposed to just "conformation". I'm wondering if there is a consensus on the precise meaning of topology in the genomics/Hi-C context.