A note on knot Floer homology of satellite knots with (1,1)-patterns

Weizhe Shen

We prove that if $P$ is a $(1,1)$-pattern knot, the two inequalities $\dim \widehat{HFK}(P(K))⩾\dim \widehat{HFK}(P(U))$ and $\dim \widehat{HFK} (P(K)) \geqslant \dim \…