n-quasi-isotopy: III. Engel conditions
| dc.creator | Melikhov, Sergey A. | |
| dc.creator | Mikhailov, Roman V. | |
| dc.date | 2002-01-04 | |
| dc.date | 2003-08-15 | |
| dc.date.accessioned | 2026-07-07T04:45:40Z | |
| dc.date.available | 2026-07-07T04:45:40Z | |
| dc.description | In part I it was shown that for each k>0 the generalized Sato-Levine invariant detects a gap between k-quasi-isotopy of link and peripheral structure preserving isomorphism of the finest quotient G_k of its fundamental group, `functorially' invariant under k-quasi-isotopy. Here we show that Cochran's derived invariant β^k, provided k>2, and a series of \barμ-invariants, starting with \barμ(111112122) for k=3, also fall in this gap. In fact, all \barμ-invariants where each index occurs at most k+1 times, except perhaps for one occuring k+2 times, can be extracted from G_k, and if they vanish, G_k is the same as that of the unlink. We also study the equivalence relation on links (called `fine k-quasi-isotopy') generated by ambient isotopy and the operation of interior connected sum with the second component of the (k+1)-th Milnor's link, where the complement to its first component is embedded into the link complement. We show that the finest quotient of the fundamental group, functorially invariant under fine k-quasi-isotopy is obtained from the fundamental group by forcing all meridians to be (k+2)-Engel elements. We prove that any group generated by two 3-Engel elements has lower central series of length <6. | |
| dc.description | 24 pages, 7 figures | |
| dc.identifier | https://arxiv.org/abs/math/0201022 | |
| dc.identifier | http://arxiv.org/abs/math/0201022 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63037 | |
| dc.subject | Geometric Topology | |
| dc.subject | Group Theory | |
| dc.subject | 57M25; 20F45 | |
| dc.title | n-quasi-isotopy: III. Engel conditions | |
| dc.type | text |