Geodesic
Floer homology and splicing knot complements
Eftekhary, Eaman1
1School of Mathematics, Institute for Research in Fundamental Sciences (IPM), PO Box 19395-5746, Tehran 19395, Iran
Algebraic and Geometric Topology, Tome 15 (2015) no. 6, pp. 3155-3213
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We obtain a formula for the Heegaard Floer homology (hat theory) of the three-manifold Y (K1,K2) obtained by splicing the complements of the knots Ki ⊂ Y i, i = 1,2, in terms of the knot Floer homology of K1 and K2. We also present a few applications. If hni denotes the rank of the Heegaard Floer group HFK̂ for the knot obtained by n–surgery over Ki, we show that the rank of HF̂(Y (K1,K2)) is bounded below by

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

DOI : 10.2140/agt.2015.15.3155
Classification : 57M27, 57R58
Keywords: Floer homology, splicing, essential torus

Eftekhary, Eaman  1

1 School of Mathematics, Institute for Research in Fundamental Sciences (IPM), PO Box 19395-5746, Tehran 19395, Iran 
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Eftekhary, Eaman. Floer homology and splicing knot complements. Algebraic and Geometric Topology, Tome 15 (2015) no. 6, pp. 3155-3213. doi: 10.2140/agt.2015.15.3155

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