Computes the k-skeleton of the mapper by computing the nerve of the pullback of cover member.

## Arguments

k the maximal dimension to consider.

## Details

The primary output of the Mapper method is a simplicial complex. With MapperRef objects, the simplicial complex is stored as a simplextree. The underlying complex does not need to be modified by the user, i.e. is completely maintained by MapperRef methods (e.g. this method, construct_nerve, etc.).

This function computes the k-skeleton inductively, e.g. by first computing the vertices, then the edges, etc. up to the dimension specified. A check is performed to ensure the pullback has been decomposed, and if not, then construct_pullback is called.

For an algorithmic description of this process, see Singh et. al, section 3.2.

## References

Gurjeet Singh, Facundo Mémoli, and Gunnar Carlsson. "Topological methods for the analysis of high dimensional data sets and 3d object recognition." SPBG. 2007.