We obtain a formula for the Heegaard Floer homology (hat theory) of
the threemanifold Y(K_{1},K_{2}) obtained by splicing the complements of the
knots K_{i} ⊂ Y_{i}, i=1,2, in terms of the knot Floer
homology of K_{1} and K_{2}. We also present a few applications. If h_{n}^{i} denotes
the rank of the Heegaard Floer group \ov\HFKT for the knot obtained by nsurgery
over K_{i} we show that the rank of \ov\HFT(Y(K_{1},K_{2})) is bounded below by
 ⎢ ⎢

(h_{∞}^{1}−h_{1}^{1})(h_{∞}^{2}−h_{1}^{2})−(h_{0}^{1}−h_{1}^{1})(h_{0}^{2}−h_{1}^{2})  ⎢ ⎢

. 

We also show that if splicing the complement of a knot K ⊂ Y with the trefoil
complements gives a homology sphere Lspace then K is trivial and Y is a homology
sphere Lspace.
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