[ Generalized Jordan curve to prove that there is a boundary .... although it’s not a connected graph ]
Boundary of boundary:
This was an example of boundary of a boundary = 0.
We can do a generalization of this by looking at which is reached from each node from pairs of edges, not just single edges. Instead of asking about a single geodesic coming from the outside into the inside region, asking about p geodesics doing this, and then record all p-tuples of points where these geodesics first intersect the inside region.
(Helmholtz decomposition theorem) Decompose any vector field into a divergence free and curl free part.
[ Making a p form from a collection of p edges without knowing which edge is which naturally leads to an antisymmetric object ]
In the case of a grid, we label the coordinates by real numbers
In the case of a tree, we can natural;y use p-adic numbers
Are spinors like directed edges ; vectors like undirected edges ??
Directed edge needs to be doubled to make an undirected edge....
Inverse square law
1/(area of d-dimensional sphere)
Quantum Field Theory
[ Renormalization seems to be very 4 dimensional ] [ Dimensional regularization ]
[ Hard to do in d dimensions]
Some don’t depend on dimension; others, like G, do.