AlgebraicJulia / CombinatorialSpaces.jl

Simplicial sets and other combinatorial models of geometric spaces
MIT License
27 stars 4 forks source link

Laplacians for generic simplicial sets #94

Open lukem12345 opened 1 month ago

lukem12345 commented 1 month ago

Currently, we offer two versions of the Laplace operator - de Rham and Beltrami - for each form and each dimension of delta dual complex.

However, we do not generate Laplacians for simplicial sets. This is useful for doing things like opinion dynamics.

We should use our boundary and coboundary matrices to generate Laplacians for simplicial sets, even those without metric information available.

jpfairbanks commented 1 month ago

Is this just

A = boundary(X)*coboundary(X)
L = diag(A) - A
lukem12345 commented 1 month ago

Yes