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Plumbing is a natural operation in Khovanov homology
[article]
2017
arXiv
pre-print
Given a connect sum of link diagrams, there is an isomorphism which decomposes unnormalized Khovanov chain groups for the product in terms of normalized chain groups for the factors; this isomorphism is straightforward to see on the level of chains. Similarly, any plumbing x*y of Kauffman states carries an isomorphism of the chain subgroups generated by the enhancements of x*y, x, y: C_R(x*y)→(C_R,p→1(x)⊗C_R,p→1(y))⊕(C_R,p→0(x)⊗C_R,p→0(y)). We apply this plumbing of chains to to prove that
arXiv:1705.01931v1
fatcat:hnrohbcg7neo7h7orhdhethnvy