Georgia Institute of Technology College of Sciences

Given two knots K_1 and K_2, their 0-surgery manifolds S_0^3(K_1) and S_0^3(K_2) are homology cobordant rel meridian if they are homology cobordant preserving the homology class of the positively oriented meridian. It is known that if K_1 ∼ K_2, then S_0^3(K_1) and S_0^3(K_2) are homology cobordant rel meridian. The converse of this statement was first disproved by Cochran-Franklin-Hedden-Horn.  In this talk we will provide a new counterexample, the pair of knots 4_1 and M(4_1) where M is the Mazur satellite operator. S_0^3(4_1) and S_0^3(M(4_1)) are homology cobordant rel meridian, but 4_1 and M(4_1) are non-concordant and have concordance orders 2 and infinity, respectively.