Curves In 3-Manifolds

This project looked at how to present geometric ideas in ways that suitable for a wider audience. In particular, we focused on ways to generate visual depictions of the homologous generators of the space of specific Seifert fiberings. The results displayed on this site are largely outlined in this paper.

Acknowledgments

This project was completed in part with the Illinois Mathematics Lab at the University of Illinois Urbana-Champaign. In particular, we’d like to thank our graduate mentor Shana Li for her guidance throughout the course of this project. We’d also like to thank Yi Wang for his mentorship as well as providing the paper which provided the theoretical basis for much of this project.

More Information

For an introductory explanation of these animations, refer to this article.

Additionally, you can find on this album a collection of all the images we’ve generated over the course of a semester.

You can also find the code to generate some images on your own in this GitHub repository. Here’s also a link for the site source if anyone has any suggestions.