SoaPy is a Python package intended to facilitate the life of anyone working with Seifert fibered rational homology spheres (SFS). The package allows the user to work with the class soapy.SFS as well as its subclasses soapy.Lens, soapy.Prism and soapy.Brieskorn. For a given SFS Y, the package allows one to find, among other things,
- a definite plumbing description of Y;
- the corresponding linking matrix;
- the first homology of Y;
- HF^+(Y); and
- the Casson-Walker invariant of Y.
Moreover, the package allows one to check if a given pair Y_1 and Y_2 of SFS passes a certain obstruction to there existing an ribbon rational homology cobordism from Y_1 to Y_2.
Lastly, the package comes with built-in functions to check if a given SFS is homeomorphic to a lens space or a prism manifold, and if two different parametrizations of a SFS actually represent the same SFS.
For instructions and underlying mathematical conventions, refer to the PDF.
For required packages, refer to requirements.txt. Alternatively, you can use the "pipenv" package manager and the Pipfile included to install a virtual environment and import the package as follows.
cd SoaPy
pipenv install
pipenv shell
python3
>>> import soapy as sp