We first show that the three-variable bracket polynomial is an invariant for reduced, alternating links. We then try to find what the polynomial reveals about knots. We find that the polynomial gives the crossing number, a test for chirality, and in some cases, the twist number of a knot. The extreme degrees of d are also studied.

Author Bio

Kelsey Lafferty is a senior at Wheaton College in Wheaton, IL. She completed this work during the 2013 REU at California State University, San Bernardino under the guidance of Dr. Rolland Trapp. After graduation in May 2014, she plans to attend graduate school with the goal of obtaining a Ph.D. in mathematics.