Ribbon-moves of 2-links preserve the μ-invariant of 2-links
| dc.creator | Ogasa, Eiji | |
| dc.date | 2000-04-02 | |
| dc.date.accessioned | 2026-07-07T04:34:36Z | |
| dc.date.available | 2026-07-07T04:34:36Z | |
| dc.description | 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 ones.) Let L_1 and L_2 be 2-links. Then the following hold. (1) If L_1 is ribbon-move equivalent to L_2, then we have μ(L_1)=μ(L_2). (2) Suppose that L_1 is ribbon-move equivalent to L_2. Let W_i be arbitrary Seifert hypersurfaces for L_i. Then the torsion part of H_1(W_1)+H_1(W_2) is congruent to G+G for a finite abelian group G. (3) Not all 2-knots are ribbon-move equivalent to the trivial 2-knot. (4) The inverse of (1) is not true. (5) The inverse of (2) is not true. Let L=(L_1,L_2) be a sublink of homology boundary link. Then we have: (i) L is ribbon-move equivalent to a boundary link. (ii) μ(L)= μ(L_1) + μ(L_2). We would point out the following facts by analogy of the discussions of finite type invariants of 1-knots although they are very easy observations. By the above result (1), we have: the μ-invariant of 2-links is an order zero finite type invariant associated with ribbon-moves and there is a 2-knot whose μ-invariant is not zero. The mod 2 alinking number of (S^2, T^2)-links is an order one finite type invariant associated with the ribbon-moves and there is an (S^2, T^2)-link whose mod 2 alinking number is not zero. | |
| dc.description | 13 pages 21 figures | |
| dc.identifier | https://arxiv.org/abs/math/0004008 | |
| dc.identifier | http://arxiv.org/abs/math/0004008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58965 | |
| dc.subject | Geometric Topology | |
| dc.subject | Mathematical Physics | |
| dc.subject | 57M25, 57Q45, 57R65 | |
| dc.title | Ribbon-moves of 2-links preserve the μ-invariant of 2-links | |
| dc.type | text |