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

2022/07/05 by Weizhe Shen, Shen, Weizhe
Mathematics · Medicine · Biochemistry, Genetics and Molecular Biology · #Geometric and Algebraic Topology #Botulinum Toxin and Related Neurological Disorders #Cellular transport and secretion

paper · pdf · doi:10.48550/arxiv.2207.01787

Abstract

We prove that if P is a (1,1)-pattern knot, the two inequalities dim \widehatHFK (P(K)) \geqslant dim \widehatHFK (P(U)) and dim \widehatHFK (P(K)) \geqslant dim \widehatHFK (K) hold for the unknot U⊂ S³ and any companion knot K⊂ S³.

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