Knot Floer homology of satellite knots with (1,1)-patterns

2019/12/17 by Chen, Wenzhao
#57M25 #57R58 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1912.07914

Abstract

For pattern knots admitting genus-one bordered Heegaard diagrams, we show the knot Floer chain complexes of the corresponding satellite knots can be computed using immersed curves. This, in particular, gives a convenient way to compute the τ-invariant. For patterns P obtained from two-bridge links b(p,q), we derive a formula for the τ-invariant of P(T_2,3) and P(-T_2,3) in terms of (p,q), and use this formula to study whether such patterns induce homomorphisms on the concordance group, providing a glimpse at a conjecture due to Hedden.

Related

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