2016/08/25 by Ni, Yi, Vafaee, Faramarz
#FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1608.07050
Let K be a knot in an L-space Y with a Dehn surgery to a surface bundle over S1. We prove that K is rationally fibered, that is, the knot complement admits a fibration over S1. As part of the proof, we show that if K⊂ Y has a Dehn surgery to S1 × S2, then K is rationally fibered. In the case that K admits some S1 × S2 surgery, K is Floer simple, that is, the rank of HFK(Y,K) is equal to the order of H1(Y). By combining the latter two facts, we deduce that the induced contact structure on the ambient manifold Y is tight. In a different direction, we show that if K is a knot in an L-space Y, then any Thurston norm minimizing rational Seifert surface for K extends to a Thurston norm minimizing surface in the manifold obtained by the null surgery on K (i.e., the unique surgery on K with b1>0).