simpcomp is an official extension to the computer algebra system GAP, that is, simpcomp is part of every full GAP installation. The software allows the user to compute numerous properties of abstract simplicial complexes such as the f -, g- and h-vectors, the fundamental group, the automorphism group, (co-)homology, the intersection form, and many more. It provides functions to generate simplicial complexes from facet lists, orbit representatives, or permutation groups. In addition, functions related to slicings and polyhedral Morse theory as well as a combinatorial version of algebraic blowups and the possibility to resolve isolated singularities of 4-manifolds are implemented.

In this talk, I will give an overview over the existing features of the software and also discuss some ongoing projects such as (i) support for Forman’s discrete Morse theory for homology and fundamental group computations, and (ii) an extension of the features to analyse tightness of triangulated manifolds.