You are welcome,
these Tools are not very complicated generally. The E8 is an exceptional Lie Group, you can see its geometry on internet, it is relevant. It is a geometrical algebras in fact and a good tool to rank. It is utilised in strings theory also and for the geometrodynamics with points, they permit to better understand the topologies and geonetries.
The poincare conjecture is a conjecture about the sphere and the charcterizations if I can say and it is about the homeomorphisms of 3 sphere , perelman has proved this conjecture and it is relevant about the deformations of spheres. I consider it important in my theory.
The lie derivatives are for the vectors fields and tensors fields,the Lie derivative is the differential of the representation of the diffeomorphism group on tensor fields,and they are correlated with Lie algebras, so see also the links with the E8 and my fractal of spheres considering the finite primordial series and the 3 E8. The spinors can be correlated also.
The topological spaces are a set of points and if you consider the spheres instead of points for the E8 , that becomes relevant for the convergences topological and geonetrical and even algebrical. You can study the works of Euler also, they are relevant and permit to converge like the works of Gauss about the curved spaces.
The euclidian space is a classical geometry simply and that becomes very relevant considering the 3D , that converges with the topological spaces, here we consider mainly the angles, distances, lenghts and when you converge with the other Tools that I have cited, it becomes very relevant to rank generally the spheres.
The Ricci flow is about a kind of deformation of spheres and I consider mainly the 3D spheres , Hamilton is relevant for this Ricci flow and it is the tool mainly utilised by Perelman to prove the poincare conjecture. The relevance in my model is that we can create all geonetries with these spheres in 3D and also we consider a main intrinsic code inside the particles , it is totally different than for the strings considering a main field and strings at this planck scale creating all our geonetries, topologies, properties of matters.The codes are inside the gfinite series, primordial of these 3 E8.
Hope that helps, don t hesitate to ask questions,
regards