Heegaard Floer homology, degree-one maps and splicing knot complements

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Let K denote a knot inside the homology sphere Y and K' denote a knot inside a homology sphere L-space. Let X=Y(K,K') denote the 3-manifold obtained by splicing the complements of K and K'. We show that rank(HF(X)) ≥ rank(HF(Y)).