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Knot Theory, a field of Topology, can be used to model and understand how enzymes (called topoi- somerases) work in DNA processes to untangle or repair strands of DNA. In a human cell nucleus, the DNA is linear, so the knots can slip off the end, and it is difficult to recognize what the enzymes do. However, the DNA in mitochondria is circular, along with prokaryotic cells (bacteria), so the enzyme processes are more noticable in knots in this type of DNA. Invariants prove to be a useful tool in studying when two knots are different. Tricolorability is an easily understood invariant that we will use to distinguish doubles (replications) of certain prime knots.
Double of knots