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

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dc.creatorOgasa, Eiji
dc.date2004-07-09
dc.date.accessioned2026-07-07T05:10:09Z
dc.date.available2026-07-07T05:10:09Z
dc.descriptionWe 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 ${\mathrm {Tor}} H_1(\widetilde X_K; {\Z})$ (resp. ${\mathrm {Tor}} H_1(\widetilde X_{K'}; {\Z})$) be the $\Z$-torsion submodule of the Alexander module $H_1(\widetilde X_K; {\Z})$ (resp. $H_1(\widetilde X_{K'}; {\Z})$). Then ${\mathrm {Tor}} H_1(\widetilde X_K; {\Z})$ is isomorphic to ${\mathrm {Tor}} H_1(\widetilde X_{K'}; {\Z})$ 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 $\tildeη$ invariants for $K$ is equivalent to that for $K'$.
dc.description8 pages 2 figures
dc.identifierhttps://arxiv.org/abs/math/0407164
dc.identifierhttp://arxiv.org/abs/math/0407164
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71839
dc.subjectGeometric Topology
dc.subjectMathematical Physics
dc.subject57M25, 57Q45, 57R65
dc.titleRibbon-moves of 2-knots: the torsion linking pairing and the $\widetildeη$-invariants of 2-knots
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