Topological Helicity for Framed Links
Student author: Elizabeth Bouzarth
Journal of Knot Theory and Its Ramifications
We introduce topological helicity, an invariant for oriented framed links. Topological helicity provides an elementary means of computing helicity for a magnetic flux rope by measuring its knotting, linking, and twisting. We present an equivalence relation, reconnection-equivalence, for framed links and prove that topological helicity is a complete invariant for the resulting equivalence classes. We conclude by showing that one can use magnetic reconnection to transform one collection of linked flux ropes into another collection if and only if they have the same helicity.
Bouzarth, Elizabeth L., and David Richeson. "Topological Helicity for Framed Links." Journal of Knot Theory and Its Ramifications 13, no. 8 (2004): 1007-1019. https://www.worldscientific.com/doi/abs/10.1142/S0218216504003664