Abstract: A braided link is the link formed by a braid closure along with the braid’s axis. The bi-orderability of such links is equivalent to asking whether or not the free group automorphism induced by the braid preserves a bi-ordering of the free group. Kin-Rolfsen produced many examples of both order-preserving and non-order-preserving braids including a complete classification of periodic braids. In our project, we use algorithmic techniques to expand the library of examples of both order-preserving and non-order-preserving braids. This work is partially funded by the NSF grant DMS-2213213. Part of this research was conducted using computational resources and services at the Center for Computation and Visualization, Brown University. This work is joint with Nancy Scherich and Hannah Turner.
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