A geometric classification of the path components of the space of locally stable maps S-3 -> R-4
2007 (English)In: Topology, ISSN 0040-9383, Vol. 46, no 6, 577-597 p.Article in journal (Refereed) Published
Locally stable maps S-3 -> R-4 are classified up to homotopy through locally stable maps. The equivalence class of a map f is determined by three invariants: the isotopy class or (f) of its framed singularity link, the generalized normal degree v (f), and the algebraic number of cusps k(f) of any extension of f to a locally stable map of the 4-disk into R-5. Relations between the invariants are described, and it is proved that for any sigma, v, and k which satisfy these relations, there exists a map f : S-3 -> R-4 with sigma(f) = sigma, v(f) = v, and k(f) = k. It follows in particular that every framed link in S3 is the singularity set of some locally stable map into R-4.
Place, publisher, year, edition, pages
2007. Vol. 46, no 6, 577-597 p.
stable map, singularity, Whitney umbrella, cusp, framed link, normal degree, immersion, regular homotopy
IdentifiersURN: urn:nbn:se:uu:diva-113052DOI: 10.1016/j.top.2006.12.004ISI: 000251603500003OAI: oai:DiVA.org:uu-113052DiVA: diva2:289818