Don't read that. That's one of the most horrible papers I know, a hodgepodge of mathematical well-known concepts thrown together with some vague ideas how they connect. The mathematical parts are explained better in any undergraduate book. I'm not sure why the author felt the need to expound on what a manifold is when that has been done better in hundreds of other texts - literally.
And it lacks a definite conclusion: They don't prove anything, don't make any particular experiment, but just loosely talk about how these ideas might be relevant to machine learning.
I'm surprised that such highly cited researcher have produced such a paper. I would be embarrassed to be on it - and I'm embarrassed on behalf of the ML community that they are citing it.
- Geometric Deep Learning Grids, Groups, Graphs, Geodesics, and Gauges: https://geometricdeeplearning.com/