curious little things

Regina the normal surface theory calculator is an extensible open-source package that implements, among other things, Rubinstein's 3-sphere recognition algorithm.

Recently I have added 3 classes to Regina: NMarkedAbelianGroup, NHomMarkedAbelianGroup, NHomologicalData. The first two classes allow one to do various homological computations for chain complexes and homomorphisms of chain complexes. NHomologicalData at present primarily implements the torsion linking form for an orientable 3-manifold, together with the Kawauchi-Kojima classification of torsion linking forms. In the future I intend to expand NHomologicalData to be able to compute the homology of abelian covers, Poincare duality in covers, Alexander polynomials of abelian covers, etc.

Nathan Dunfield's computational topology resource page.