Determinants of Rational Tangles and Their Closures

Abstract

Knot theory is a field of topology that studies the embedding of a circle in R3. In various biological processes, strands of DNA can be represented with knots. In these instances it is useful to view DNA strands topologically and model the operations mathematically to get a better understanding of what the enzymes involved in these processes are doing. The actions of these enzymes, called topoisomerases, on DNA can be represented with topological operations. This is helpful to molecular biologists in analyzing DNA and working on it to solve genetics related issues and cure genetic diseases. Our research team studied rational tangles, which can be thought of as two tangled strings with fixed ends. We researched the colorability of rational tangles. Colorability is an invariant of a tangle, so it is very helpful to understand more about it.