Cables of the figure-eight knot via real Frøyshov invariants

Geometry & Topology 2026 Open access

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Authors: Sungkyung Kang, JungHwan Park, Masaki Taniguchi
DOI: 10.2140/gt.2026.30.781
Cited by: 0
References: 61

Abstract

We prove that the .2n;1/-cable of the figure-eight knot is not smoothly slice when n is odd, by using the real Seiberg-Witten Frøyshov invariant of Konno, Miyazawa and Taniguchi.For the computation, we develop an O.2/-equivariant version of the lattice homotopy type, originally introduced by Dai, Sasahira and Stoffregen.This enables us to compute the real Seiberg-Witten Floer homotopy type for a certain class of knots.Additionally, we present some computations of Miyazawa's real framed Seiberg-Witten invariant for 2-knots.

Fields of Study & Subjects

Geometric and Algebraic Topology semigroups and automata theory Advanced Numerical Analysis Techniques

Publication details

Journal / source
Geometry & Topology
Volume
30
Issue
2
Pages
781–833
Publication date
16 March 2026
Language
EN