Regina for 3-Manifolds
macOS / Education
This app is for research mathematicians in low-dimensional topology.
Have you encountered 3-manifolds and normal surfaces, or heard about the desktop software packages Regina or SnapPy? If so, then you might find this app useful. If not, but if you are curious as to what it's all about, you might like to read about the Poincaré conjecture (http://www.claymath.org/millenium-problems/poincaré-conjecture), or hunt down a copy of Jeffrey Weeks' excellent book "The Shape of Space".
Regina is a software package for low-dimensional topologists, with a focus on 3-manifold and 4-manifold triangulations, knots and links, normal surfaces, and angle structures. For 3-manifolds, it includes high-level tasks such as 3-sphere and unknot recognition, connected sum decomposition and Hakenness testing, comes with a rich database of census manifolds, and incorporates the SnapPea kernel for working with hyperbolic manifolds. For 4-manifolds, Regina offers several combinatorial and algebraic tools, as well as support for normal hypersurfaces. For knots and links, Regina can perform combinatorial manipulation, compute knot polynomials, handle virtual knots and links, and work with several import/export formats. Advanced users can also access Regina's mathematical engine using Python scripting.
This App Store version is almost identical to the macOS app that you can download from the Regina website. The main difference is that it is sandboxed, which is excellent for security but which limits your ability to read and write arbitrary files from Python.
If you have any questions, requests or feedback then please contact Ben or the Regina development team – see http://regina-normal.github.io/ for details.
Quoi de neuf dans la dernière version ?
Regina 7.4 adds many new features, including:
- Virtual knots and links, with new invariants such as odd writhe, arrow polynomials, affine index polynomials, and extended groups;
- Several new constructions, such as Whitehead doubles over links, doubling triangulations over their boundaries, and many new out-of-the-box example triangulations and links;
- Several new operations on triangulations and link diagrams, including improving treewidth, truncating individual vertices in 3-D, and more elementary moves in more dimensions;
- New invariants and properties for link diagrams, including Alexander polynomials, Seifert circles, and connected diagram components;
- Significantly better simplification for 4-D triangulations, including Rhuaidi Burke's "up-side-down" simplification heuristics;
- More text codes for link diagrams, including signed Gauss codes and an extension of Regina's knot signatures to multiple-component links;
- Locks for top-dimensional simplices and their facets in a triangulation, which prevent them from being modified during operations such as simplification or elementary moves;
- Many, many other smaller features and optimisations.
Some other notes:
- The graphical user interface has had a general glow-up, and now offers initial support for multithreaded computations.
- The tool DGT is now called Katie, and can now work with 1-handles (thanks again to Rhuaidi Burke).
- This version fixes the occasional problem where the "try harder" option for simplifying triangulations could make the user interface crash.
Enjoy!
