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

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

2004-07-09

arxiv.org/abs/math/0407164v1

Mathematics

Geometric Topology

8 pages 2 figures

Scientific paper

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 ${\mathrm {Tor}} H_1(\widetilde X_K; {\Z})$ (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 $\tilde\eta$ invariants for $K$ is equivalent to that for $K'$.

Affiliated with

Also associated with

No associations

Rating

Ribbon-moves of 2-knots: the torsion linking pairing and the $\widetildeη$-invariants of 2-knots does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Ribbon-moves of 2-knots: the torsion linking pairing and the $\widetildeη$-invariants of 2-knots, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ribbon-moves of 2-knots: the torsion linking pairing and the $\widetildeη$-invariants of 2-knots will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-726014