Hyperbolicity equations for knot complements

Christopher Martin Jacinto

The manuscript of this item is available at https://scholarworks.lib.csusb.edu/etd-project/4414/


This study analyzes Carlo Petronio's paper, An Algorithm Producing Hyperbolicity Equations for a Link Complement in S³. Using the figure eight knot as an example, we will explain how Petronio's algorithm was able to decompose the knot complement of an alternating knot into tetrahedra. Then, using the vertex invariants of these tetrahedra, we will explain how Petronio was able to create hyperbolicity equations.