Project to incorporate Frank Lutz's data

[jspreer]

@antonydellavecchia and @micjoswig

Idea

Add functionality to SimplicialComplex so we can avoid creating an extra type.

We need:

• way to compute automorphism group of a simplicial complex (this should work with minimal effort by computing vertex facet incidence matrix and using function "automorphism_group")
• function to compute orbit representatives from automorphism group, facet list pair
• meta data for SimplicialComplex
• Field for topological type (a string, optional, could be combined with existing functionality)

How would we save data (example):

From manifold page:

facets=[[1,2,4],[1,2,6],[1,3,4],[1,3,7], [1,5,6],[1,5,7],[2,3,5],[2,3,7],[2,4,5], [2,6,7],[3,4,6],[3,5,6],[4,5,7],[4,6,7]] tt = "torus"

c = SimplicialComplex(facets) f_vector(c) hom = [] for i in 1:dim(c)+1 push!(hom,homology(c,i-1)) end automorphism_group(c) top_type(c) = tt

save(c)

[antonydellavecchia]

We should make smaller issues from this one and make a clearer roadmap, but after the release of Oscar 1.0

[simpcomp-team]

Summary of our meeting from July 16, 2024:

• We will start with creating .json files for surface triangulations from https://www3.math.tu-berlin.de/IfM/Nachrufe/Frank_Lutz/stellar/surfaces.html
• Next step is to write OSCAR files to access this data
• Roadmap: turn this into a data base, decide where to store this data, larger collections of data should probably directly be stored in a database without a separate file for each simplicial complex.

[fingolfin]

How does this relate to the GAP package simpcomp, which we already ship with OSCAR -- does it overlap with this in any way?

[micjoswig]

@jspreer is behind simpcomp, which is mostly code and little data.

Those data, currently existing on a web page at TU Berlin, are mere data. The goal is to make that OSCAR accessible.

So; no overlap.