Generating Minimal Boundary Maps
Marian Anton, Landon Renzullo · Mathematics and Statistics · 2018
The field of computational topology is evolving rapidly and new algorithms are updated and released at a rapid pace. A good reference for currently available opensource libraries with peer-review publication can be found in [7]. In this paper we examine the descriptive potential of a combinatorial data structure known as Generating Set in constructing the boundary maps of a simplicial complex. By refining the approach of [1] in generating these maps, we provide algorithms that allow for relations among simplices to be easily accounted for. In this way we explicitly generate faces of a complex only once, even if a face is shared among multiple simplices. The result is a useful interface for constructing complexes with many relations and for extending our algorithms to ∆-complexes. Once we efficiently retrieve the representatives of