Implement finite covers of simplicial sets

[miguelmarco]

This branch implements the computation of finite covers of simplicial sets, and also the simplicial set associated to a grpup presentation.

CC: @jhpalmieri

Component: algebraic topology

Author: Miguel Marco

Issue created by migration from https://trac.sagemath.org/ticket/34886

[miguelmarco]

Branch: u/mmarco/simplicial_set_group

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

[sagetrac-git]

Commit: 2114066

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

59b4f54

Implementation of simplicial set covers and simplicial stes of group presentations

[sagetrac-git]

Changed commit from 2114066 to 59b4f54

[miguelmarco]

Author: Miguel Marco

[jhpalmieri]

comment:5

I like this. A few questions:

• is it possible to reduce the code duplication between fundamental_group and universal_cover_map?

• can you provide more documentation for PresentationComplex, in particular a definition of what the complex is?

[dimpase]

comment:6

I wonder whether this would work for "graphs with constant link" - the complex with be given by vertices, edges, and triangles of a graph; one famous in graph theory examples are "locally Petersen graphs"; e.g. the 21-vertex graph with vertices being pairs of elements of a 7-element set, two vertices adjacent if the corr. pairs don't intersect. In Sage one can get it as
graphs.JohnsonGraph(7,2).complement()

In this case there is a universal 3-fold cover - corresponding to a subgroup of the Schur multiplier of the alternative group Alt(7), which is an automorphism group of this graph.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

9be1db0

Deduplicate code in fundamental group and universal cover

[sagetrac-git]

Changed commit from 59b4f54 to 9be1db0