Heegaard Floer Homology, Degree-One Maps and Splicing Knot Complements

Suppose that K and K' are knots inside the homology spheres Y Y', respectively. Let X = (K, K') be 3-manifold obtained by splicing complements of Z three-manifold 0 surgery on K. When Y' is an L-space, we use formula [1] to show rank (X ) bounded below (Y if τ(K 2 rank( (Z)) − (Y)) + 1 τ(K') ≠ 0.