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Khovanov Homology on Symmetric Unions of Certain 2-Bridge Knots
Symmetric unions, originally introduced in 1957 by Shin’ichi Kinoshita and Hide-
taka Terasaka , have since been studied due to their failure to be distinguished by
some invariants. In his 2000 paper, Mikhail Khovanov introduced a powerful new
invariant, Khovanov Homology, which gives more information (an entire homology)
than some more classic invariants. In this paper, we look at Khovanov Homology’s
ability to distinguish or classify symmetric unions of particular knots. We are able to
show that Khovanov Homology can, in fact, classify symmetric unions of (2,m)-torus
knots and certain other 2-bridge knots.