Rational Tangles and Braids Undergraduate Research

This blog is serving as a journal and content aggregator for my current independent study project with Dr. Eric Errthum at Winona State University. My project concerns rational tangles and their relationship to continued fractions, matrix groups, and braid groups. To be more specific, we have been exploring the action of the 3-strand braid group on 2-component rational tangles and how to expand the current theory to 2-component subsections of knots that are not rational tangles. Furthermore, we have been looking at the idea on how/if this action generalizes to an -strand braid group acting on a tangle of components, and what it would mean for these tangles to be “rational”

For those who are new to the idea of knots, tangles, and braids in mathematics, the “Help/Background” section contains pages that will explain the basic concepts and terminology used in other parts of the blog. The “News” section will contain periodic posts on what has been found out in both my weekly meetings with Dr. Errthum on Fridays, as well as my independent studies outside of those meetings. Posts from there can be found in “Friday Meeting Media” and/or “Notebook Scans” when applicable.