The Hopf invariant of a Haefliger knot
| dc.creator | Takase, Masamichi | |
| dc.date | 2005-06-17 | |
| dc.date.accessioned | 2026-07-07T07:55:27Z | |
| dc.date.available | 2026-07-07T07:55:27Z | |
| dc.description | We show that Haefliger's differentiable (6,3)-knot bounds, in 6-space, a 4-manifold (a Seifert surface) of arbitrarily prescribed signature. This implies, according to our previous paper, that the Seifert surface has been prolonged in a prescribed direction near its boundary. This aspect enables us to understand a resemblance between Ekholm-Szucs' formula for the Smale invariant and Boechat-Haefliger's formula for Haefliger knots. As a consequence, we show that an immersion of the 3-sphere in 5-space can be regularly homotoped to the projection of an embedding in 6-space if and only if its Smale invariant is even. We also correct a sign error in our previous paper: "A geometric formula for Haefliger knots" [Topology 43 (2004) 1425-1447]. | |
| dc.identifier | https://arxiv.org/abs/math/0506356 | |
| dc.identifier | http://arxiv.org/abs/math/0506356 | |
| dc.identifier | Mathematische Zeitschrift 256 (2007) pp.35-44 | |
| dc.identifier | doi:10.1007/s00209-006-0053-8 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126976 | |
| dc.subject | Geometric Topology | |
| dc.subject | Algebraic Topology | |
| dc.subject | 57R40; 57R52; 57R45 | |
| dc.title | The Hopf invariant of a Haefliger knot | |
| dc.type | text |