On rational sliceness of Miyazaki's fibered, −amphicheiral knots

2016/04/17 by Min Hoon Kim, Zhongtao Wu · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Alexander polynomial #Class (philosophy) #Floer homology #Geometric and Algebraic Topology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Knot (papermaking) #Skein relation #math.GT

paper · pdf · doi:10.1112/blms.12152

14 pages, 1 figure

arxiv created 2016/04/17 · openalex created_date 2016/06/24 · openalex publication_date 2018/04/06 · arxiv updated 2018/04/18 · openalex updated_date 2026/08/05

Abstract

We prove that fibered, −amphicheiral knots with irreducible Alexander polynomials are rationally slice. This contrasts with the result of Miyazaki that ( 2 n , 1 ) -cables of these knots are not ribbon. We also show that the concordance invariants ν + and Υ from Heegaard Floer homology vanish for a class of knots that includes rationally slice knots. In particular, the ν + - and Υ-invariants vanish for these cable knots.

Citations

• A cabling formula for the 𝜈⁺ invariant
• Knot concordance and homology cobordism
• Concordance homomorphisms from knot Floer homology
• Algebra

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