6 papers · 1 filter
Ribbon-moves of 2-knots: the torsion linking pairing and the -invariants of 2-knots
Eiji Ogasa
We discuss the ribbon-move for 2-knots, which is a local move. Let and be 2-knots. Then we have: Suppose that and are ribbon-move equivalent. (1) Let ${\mathrm {T…
n-dimensional links, their components, and their band-sums
Eiji Ogasa
We prove the following results (1) (2) (3) on relations between -links and their components. (1) Let L=(L_1, L_2) be a (4k+1)-link (4k+1\geq 5). Then we have Arf L=Arf L_1+Arf L…
Ribbon-moves of 2-links preserve the μ-invariant of 2-links
Eiji Ogasa
We introduce ribbon-moves of 2-knots, which are operations to make 2-knots into new 2-knots by local operations in B^4. (We do not assume the new knots is not equivalent to the old…
Ribbon-moves of 2-knots: the Farber-Levine pairing and the Atiyah-Patodi-Singer-Casson-Gordon-Ruberman -invariants of 2-knots
Eiji Ogasa
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 A…
The intersection of spheres in a sphere and a new geometric meaning of the Arf invariant
Eiji Ogasa
Let S^3_i be a 3-sphere embedded in the 5-sphere S^5 (i=1,2). Let S^3_1 and S^3_2 intersect transversely. Then the intersection C of S^3_1 and S^3_2 is a disjoint collection of cir…
The projections of n-knots which are not the projection of any unknotted knot
Eiji Ogasa
Let n be any integer greater than two. We prove that there exists a projection P having the following properties. (1) P is not the projection of any unknotted knot. (2) The singula…