![]() | The Regina Handbook |
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Copyright © 1999–2020 The Regina development team
Both Regina and this handbook are licensed under the terms of the GNU General Public License.
Regina is a software package for 3-manifold and 4-manifold topologists, with a focus on 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, it offers a range of combinatorial and algebraic tools, plus support for normal hypersurfaces. Regina comes with a full graphical user interface, as well as Python bindings and a low-level C++ programming interface.
The current version of Regina is 5.96 (the first prerelease before version 6.0). This handbook is still being updated for version 6.0, and most of the material here is from the (much older) version 5.1.
Tip: You can also browse the alphabetical index of tasks.
Table of Contents
- 1. Introduction
- 2. Working with Packets
- 3. Triangulations
- Creation
- Analysis
- Identifying the Manifold (2-D and 3-D)
- Validity, Orientability and Other Basic Properties (All Dimensions)
- Viewing Facet Gluings (All Dimensions)
- Skeletal Information (All Dimensions)
- Algebraic Invariants (3-D and 4-D)
- Combinatorial Composition (3-D)
- High-Level Recognition Routines (3-D)
- SnapPea Calculations (3-D)
- Decomposition (All Dimensions)
- Triangulating Vertex Links (3-D and 4-D)
- Triangulating Boundary Components (3-D and 4-D)
- Modification
- Editing Gluings (All Dimensions)
- Automatic Simplification (3-D and 4-D)
- Manual Simplification: Elementary Moves (3-D and 4-D)
- 0-Efficiency (3-D)
- Switching Between Real and Ideal (3-D and 4-D)
- Subdivision (All Dimensions)
- Orienting Triangulations and Double Covers (All Dimensions)
- Puncturing and Drilling (3-D)
- Building Connected Sums (3-D)
- Cutting Along and Crushing Normal Surfaces (3-D)
- 4. SnapPea Triangulations
- 5. Normal Surfaces and Hypersurfaces
- 6. Angle Structures
- 7. Knots and Links
- 8. Importing and Exporting Data
- 9. Python Scripting
- 10. Configuration
- 11. Compiling Regina Into Your Projects
- 12. Troubleshooting and FAQ
- 13. Bug Tracking and Feature Requests
- A. Command Line: Main Applications
- regina-gui - Regina's graphical user interface
- regina-python - Regina's command-line Python interface
- B. Command Line: Specialised Utilities
- censuslookup - Search for triangulations in Regina's census databases
- regconcat - Combine several Regina data files
- regconvert - Convert between different Regina file formats
- regfiledump - Dump the contents of a Regina data file
- regfiletype - Identify the formats of Regina data files
- retriangulate - Exhaustively retriangulate a given manifold
- sigcensus - Form a census of splitting surface signatures
- tricensus - Form a census of triangulations
- trisetcmp - Compare triangulations between two Regina data files
- C. Version History
- D. Authors and License
- Index
- Bibliography
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