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A geometric classification of the path components of the space of locally stable maps S-3 -> R-4
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2007 (English)In: Topology, ISSN 0040-9383, E-ISSN 1879-3215, Vol. 46, no 6, 577-597 p.Article in journal (Refereed) Published
Abstract [en]

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.
Keyword [en]
stable map, singularity, Whitney umbrella, cusp, framed link, normal degree, immersion, regular homotopy
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-113052DOI: 10.1016/j.top.2006.12.004ISI: 000251603500003OAI: oai:DiVA.org:uu-113052DiVA: diva2:289818
Available from: 2010-01-25 Created: 2010-01-25 Last updated: 2017-12-12Bibliographically approved

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