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Algebra i Analiz, 1999, Volume 11, Issue 5, Pages 250–272 (Mi aa1083)  

This article is cited in 3 scientific papers (total in 3 papers)

Research Papers

Self-intersection surfaces, regular homotopy, and finite order invariants

T. Ekholm

Department of Mathematics, Uppsala University, Uppsala, Sweden

Abstract: Explicit formulas for the regular homotopy classes of generic immersions $S^k\to{\mathbb R}^{2k-2}$ are given in terms of the corresponding self-intersection manifolds with natural additional structures.
There is a natural notion of finite order invariants of generic immersions. We determine the group of $m$th order invariants for each $m$ and prove that the finite order invariants are not sufficient for distinguishing generic immersions that cannot be obtained from each other by a regular homotopy through generic immersions.

Keywords: immersion, regular homotopy, finite order invariants, spin and pin structures.

Full text: PDF file (1173 kB)

English version:
St. Petersburg Mathematical Journal, 2000, 11:5, 909–929

Bibliographic databases:

Received: 12.04.1999
Language:

Citation: T. Ekholm, “Self-intersection surfaces, regular homotopy, and finite order invariants”, Algebra i Analiz, 11:5 (1999), 250–272; St. Petersburg Math. J., 11:5 (2000), 909–929

Citation in format AMSBIB
\Bibitem{Ekh99}
\by T.~Ekholm
\paper Self-intersection surfaces, regular homotopy, and finite order invariants
\jour Algebra i Analiz
\yr 1999
\vol 11
\issue 5
\pages 250--272
\mathnet{http://mi.mathnet.ru/aa1083}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1734356}
\zmath{https://zbmath.org/?q=an:0967.57022}
\transl
\jour St. Petersburg Math. J.
\yr 2000
\vol 11
\issue 5
\pages 909--929


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Saeki, O, “Regular homotopy classes of immersions of 3-manifolds into 5-space”, Manuscripta Mathematica, 108:1 (2002), 13  crossref  mathscinet  zmath  isi  scopus
    2. Ekholm T., Szucs A., “Geometric formulas for Smale invariants of codimension two immersions”, Topology, 42:1 (2003), 171–196  crossref  mathscinet  zmath  isi  scopus
    3. Yamamoto, M, “First order semi-local invariants of stable maps of 3-manifolds into the plane”, Proceedings of the London Mathematical Society, 92 (2006), 471  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и анализ St. Petersburg Mathematical Journal
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