I’m not sure what “geometry of thought” is supposed to mean. However, I would agree that acquiring knowledge is more like drawing a map than it is like compiling a collection of facts. Philosophers, with their “knowledge = justified true belief” have made a mistake (in my opinion).
The way that knowledge is represented isn’t necessarily identical with what knowledge is. And actually, I don’t think it would be wrong to say that a map (considered as knowledge) is a collection of facts - it’s simply that those facts aren’t represented in sentential form, but instead they are represented in another way.