Ribbon-moves of 2-knots: the torsion linking pairing and the \widetildeη-invariants of 2-knots

2004/07/09 by Eiji Ogasa, Ogasa, Eiji
Mathematics · Physics and Astronomy · #57M25 #57Q45 #57R65 #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #math-ph #math.GT #math.MP #msc:57M25 #msc:57Q45 #msc:57R65

paper · pdf · doi:10.48550/arxiv.math/0407164

8 pages 2 figures

arxiv created 2004/07/09 · openalex publication_date 2004/07/09 · arxiv updated 2009/12/01 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

We discuss the ribbon-move for 2-knots, which is a local move. Let K and K' be 2-knots. Then we have: Suppose that K and K' are ribbon-move equivalent. (1) Let \mathrm Tor H₁(\widetilde X_K; \Z) (resp. \mathrm Tor H₁(\widetilde X_K'; \Z)) be the \Z-torsion submodule of the Alexander module H₁(\widetilde X_K; \Z) (resp. H₁(\widetilde X_K'; \Z)). Then \mathrm Tor H₁(\widetilde X_K; \Z) is isomorphic to \mathrm Tor H₁(\widetilde X_K'; \Z) not only as \Z-modules but also as \Z[t,t^-1]-modules. (2) The Farber-Levine pairing for K is equivalent to that for K'. (3) The set of the values of the \Q/\Z-valued η invariants for K is equivalent to that for K'.

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