uu.seUppsala University Publications
Change search
ReferencesLink to record
Permanent link

Direct link
Singular Seifert surfaces and Smale invariants for a family of 3-sphere immersions
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Geometry and Logic.
2011 (English)In: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 43, no 2, 251-266 p.Article in journal (Refereed) Published
Abstract [en]

A self-transverse immersion of the 2-sphere into 4-space with algebraic number of self-intersection points equal to-n induces an immersion of the circle bundle over the 2-sphere of Euler class 2n into 4-space. Precomposing these circle bundle immersions with their universal covering maps, we get for n > 0 immersions g(n) of the 3-sphere into 4-space. In this note, we compute the Smale invariants of g(n). The computation is carried out by (partially) resolving the singularities of the natural singular map of the punctured complex projective plane which extends g(n). As an application, we determine the classes represented by g(n) in the cobordism group of immersions which is naturally identified with the stable 3-stem. It follows in particular that g(n) represents a generator of the stable 3-stem if and only if n is divisible by 3.

Place, publisher, year, edition, pages
2011. Vol. 43, no 2, 251-266 p.
National Category
URN: urn:nbn:se:uu:diva-151903DOI: 10.1112/blms/bdq097ISI: 000288567300003OAI: oai:DiVA.org:uu-151903DiVA: diva2:411631
Available from: 2011-04-19 Created: 2011-04-19 Last updated: 2012-11-16Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Ekholm, Tobias
By organisation
Algebra, Geometry and Logic
In the same journal
Bulletin of the London Mathematical Society

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 195 hits
ReferencesLink to record
Permanent link

Direct link