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

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