Knots 2013 AMRE team

Knot Theory

Undergraduate Research in Knot Theory

Student Researchers: Joseph Smith, Michael Bush, Katelynn French,

Faculty Advisors: John Ramsay and Jennifer Bowen (Mathematics)

Our research in knot theory was funded by HHMI Undergraduate Science Research Program and The College of Wooster’s Sophomore Research Program. Our team continued the College’s past research of Klein links. We focused on looking at the invariant of linking number for Klein links, as well as for torus links. With the use of braid words, we discovered equations that can calculate the linking numbers of Klein and torus links. We have written a paper on this subject, which we hope to publish. We have begun researching the P-colorability of Klein links and have found very interesting results. We hope to better understand these results in the future. Lastly, we have investigated the effect of Klein bottle hole placement on the created Klein links. We plan on finishing the write up of our conclusions and submitting them for publication.