SnapPy is a mathematical application for studying the topology and geometry of three-dimensional manifolds, with particular emphasis on hyperbolic structures. It combines computational tools with interactive graphical facilities for investigating geometric objects, knots and links.
The application is based on the SnapPea computational kernel originally developed by Jeff Weeks. It provides a Python interface for constructing manifolds, performing geometric calculations and examining topological properties. Its graphical tools make it possible to visualise structures that would otherwise be difficult to understand through numerical results alone.
SnapPy is designed primarily for researchers and advanced students working in geometric topology, knot theory and hyperbolic geometry. It can be used independently or alongside SageMath for more extensive symbolic and numerical investigations.
This is free and open source software.
Key Features
- Study hyperbolic three-dimensional manifolds through numerical and geometric computations.
- Interactive graphical editor for creating and manipulating knot and link diagrams.
- Three-dimensional visualisation of Dirichlet domains and cusp neighbourhoods.
- Construct and modify ideal triangulations of three-dimensional manifolds.
- Calculate hyperbolic volumes, cusp shapes and other geometric invariants.
- Perform Dehn fillings to construct and investigate related manifolds.
- Compute fundamental groups, homology groups and manifold symmetry information.
- Explore extensive built-in censuses of closed and cusped hyperbolic manifolds.
- Identify manifolds by comparing their geometric properties with census entries.
- Investigate knot and link complements using specialised topological calculations.
- Support for band moves, ribbon concordances and selected knot slice obstructions.
- Calculate length spectra and investigate geodesic structures within hyperbolic manifolds.
- Verified numerical computations for selected geometric invariants and manifold properties.
- High-precision calculations for studying hyperbolic geometric structures.
- Interactive Python interface for scripting calculations and automating mathematical investigations.
- Integration with SageMath for additional algebraic and number-theoretic computations.
- Cross-platform support – runs on Linux, macOS, and Windows.
Website: snappy.computop.org
Support:
Developer: Marc Culler, Nathan Dunfield, Matthias Goerner, and contributors
License: GNU General Public License v2.0
SnapPy is written in Python. Learn Python with our recommended free books and free tutorials.
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