Let K and K' be 2-knots. Suppose that K and K' are ribbon-move equivalent.
Then the Farber-Levine pairing for K is equivalent to that for K' and the
(Z-)torsion part of the first Alexander module of $K$ is isomorphic to that of
K' as Z[Z] modules.
Let K be a 2-knot which is ribbon-move equivalent to the trivial knot. Then
the Atiyah-Patodi-Singer-Casson-Gordon-Ruberman Q/Z-valued
\widetilde\eta-invariants of K for Z_d is zero. (d is a natural number. d>2.).
@article{0004007,
author = {Ogasa, Eiji},
title = {Ribbon-moves of 2-knots: the Farber-Levine pairing and the
Atiyah-Patodi-Singer-Casson-Gordon-Ruberman $\widetilde\eta$-invariants of
2-knots},
journal = {arXiv},
volume = {2000},
number = {0},
year = {2000},
language = {en},
url = {http://dml.mathdoc.fr/item/0004007}
}
Ogasa, Eiji. Ribbon-moves of 2-knots: the Farber-Levine pairing and the
Atiyah-Patodi-Singer-Casson-Gordon-Ruberman $\widetilde\eta$-invariants of
2-knots. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0004007/