On maps with unstable singularities
| dc.creator | Melikhov, Sergey A. | |
| dc.date | 2001-01-05 | |
| dc.date | 2001-11-05 | |
| dc.date.accessioned | 2026-07-07T06:31:49Z | |
| dc.date.available | 2026-07-07T06:31:49Z | |
| dc.description | If a continuous map f: X->Q is approximable arbitrary closely by embeddings X->Q, can some embedding be taken onto f by a pseudo-isotopy? This question, called Isotopic Realization Problem, was raised by Shchepin and Akhmet'ev. We consider the case where X is a compact n-polyhedron, Q a PL m-manifold and show that the answer is 'generally no' for (n,m)=(3,6); (1,3), and 'yes' when: 1) m>2n, (n,m)\neq (1,3); 2) 2m>3(n+1) and the set {(x,y)|f(x)=f(y)} has an equivariant (with respect to the factor exchanging involution) mapping cylinder neighborhood in X\times X; 3) m>n+2 and f is the composition of a PL map and a TOP embedding. In doing this, we answer affirmatively (with a minor preservation) a question of Kirby: does small smooth isotopy imply small smooth ambient isotopy in the metastable range, verify a conjecture of Kearton-Lickorish: small PL concordance implies small PL ambient isotopy in codimension \ge 3, and a conjecture set of Repovs-Skopenkov. | |
| dc.description | 46 pages, 5 figures, to appear in Topol Appl; some important footnotes added in version 2 | |
| dc.identifier | https://arxiv.org/abs/math/0101047 | |
| dc.identifier | http://arxiv.org/abs/math/0101047 | |
| dc.identifier | Topol. Appl. 120 (2002) 105-156 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98718 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57N37 | |
| dc.title | On maps with unstable singularities | |
| dc.type | text |