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Carmen Caprau
On the universal sl(2)-link cohomology
We will discuss a geometric approach to the universal (Khovanov-type) sl(2)-link cohomology theory which depends on two formal parameters, call them h and t, and corresponds to a certain Frobenius algebra structure defined on Z[i][X, h, t]/(X2 - hX -t), where i is the primitive fourth root of unity. Our approach uses "singular" cobordisms modulo relations, bringing us a bigraded link cohomology theory which is properly functorial with respect to link cobordisms. Working over C and taking h and t to be complex numbers, the isomorphism class of the corresponding link cohomology over C is determined by the number of distinct roots of the polynomial X2 -hX -t.