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 Algebra i Analiz: Year: Volume: Issue: Page: Find

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

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.

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

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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 

• http://mi.mathnet.ru/eng/aa1083
• http://mi.mathnet.ru/eng/aa/v11/i5/p250

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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
2. Ekholm T., Szucs A., “Geometric formulas for Smale invariants of codimension two immersions”, Topology, 42:1 (2003), 171–196
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
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