Ribbon-moves of 2-knots: the Farber-Levine pairing and the Atiyah-Patodi-Singer-Casson-Gordon-Ruberman $\widetilde\eta$-invariants of 2-knots
Ribbon-moves of 2-knots: the Farber-Levine pairing and the Atiyah-Patodi-Singer-Casson-Gordon-Ruberman $\widetilde\eta$-invariants of 2-knots
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2 节的丝带移动：Farber-Levine 配对和 Atiyah-Patodi-Singer-Casson-Gordon-Ruberman $widetildeeta$ 2 节的不变量
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发表时间：
2000
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通讯作者：
Eiji Ogasa
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作者：
Eiji Ogasa
设K和K‘为2-节。假设K和K‘是带状移动等价的。则K的Farber-Levine对等价于K‘的Farber-Levine对，且$K$的第一Alexander模的(Z-)扭转部分与K’作为Z[Z]模的扭转部分同构.
设K是一个2-纽结，它的带状移动等价于平凡的纽结。则K在Z_d上的Atiyah-Patodi-Singer-Casson-Gordon-Ruberman q/Z值不变量为零。(d是自然数。D>；2.)。
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.).