Title: A link splitting spectral sequence in Khovanov Homology

Abstract: The Khovanov homology of a link L is a bigraded abelian group 
Kh(L) with Poincaré polynomial P_L(q,t), such that P(q,-1) recovers 
the Jones polynomial. The meaning of the group Kh(L) is topologically 
obscure, since its definition is resolutely combinatorial, but a suite of 
spectral sequences abutting to more manifestly three-dimensional homology 
theories provide some traction. The spectral sequence to singular 
instanton homology shows that P_L detects the unknot, and the one to 
Heegaard Floer of the branched double cover shows that P_L detects the 
two-component unlink. We construct a new spectral sequence from Kh(L) to 
the tensor product $\otimes_i Kh(K_i)$ of the Khovanov homologies of the 
components K_1,...,K_n of L. From this we show that P_L detects the 
n-component unlink for any n, and construct a novel bound on the number of 
between-component crossing changes required to split a link. This work is 
inspired by a conjectured spectral sequence in the symplectic theory of 
Seidel-Smith. Project joint with Cotton Seed.