n-dimensional links, their components, and their band-sums
| dc.creator | Ogasa, Eiji | |
| dc.date | 2000-11-21 | |
| dc.date.accessioned | 2026-07-07T04:38:44Z | |
| dc.date.available | 2026-07-07T04:38:44Z | |
| dc.description | We prove the following results (1) (2) (3) on relations between $n$-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_2. (2) Let L=(L_1, L_2) be a (4k+3)-link (4k+3\geq3). Then we have σL=σL_1+σL_2. (3) Let n\geq1. Then there is a nonribbon n-link L=(L_1, L_2) such that L_i is a trivial knot. We prove the following results (4) (5) (6) (7) on band-sums of n-links. (4) Let L=(L_1, L_2) be a (4k+1)-link (4k+1\geq 5). Let K be a band-sum of L. Then we have Arf K=Arf L_1+Arf L_2. (5) Let L=(L_1, L_2) be a (4k+3)-link (4k+3\geq3). Let K be a band-sum of L. Then we have σK=σL_1+ σL_2. The above (4)(5) imply the following (6). (6) Let 2m+1\geq3. There is a set of three (2m+1)-knots K_0, K_1, K_2 with the following property: K_0 is not any band-sum of any n-link L=(L_1, L_2) such that L_i is equivalent to K_i (i=1,2). (7) Let n\geq1. Then there is an n-link L=(L_1, L_2) such that L_i is a trivial knot (i=1,2) and that a band-sum of $L$ is a nonribbon knot. We prove a 1-dimensional version of (1). (8) Let L=(L_1, L_2) be a proper 1-link. Then Arf L =Arf L_1+ Arf L_2+{1/2}\{β^*(L)$+mod4 $\{{1/2}lk (L)\}\} =Arf L_1+Arf L_2+mod2 \{λ(L)\}, where β^*(L) is the Saito-Sato-Levine invariant and λ(L) is the Kirk-Livingston invariant. | |
| dc.description | 16 pages, no figure | |
| dc.identifier | https://arxiv.org/abs/math/0011163 | |
| dc.identifier | http://arxiv.org/abs/math/0011163 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60397 | |
| dc.subject | Geometric Topology | |
| dc.subject | Mathematical Physics | |
| dc.subject | 57M25, 57Q45, 57R65 | |
| dc.title | n-dimensional links, their components, and their band-sums | |
| dc.type | text |