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Enumeration of immersions of m-manifolds in (2m-2)-manifolds by the singularity method

Immersions And Vector Bundle Morphisms

Part of the Lecture Notes in Mathematics book series (LNM,volume 1350)

Abstract

We give an enumeration of the set of homotopy classes of monomorphisms αm↪β2m-2 for vectorbundles α,β of dimensions m and (2m-2) over a differentiable closed manifold Mm of dimension m≥6. This is applied to the classification of immersions homotopic to a map g : Mm → N2m−2. In particular we can enumerate immersions from Mm in ℝ2m−2 for all m≥6.

Keywords

  • Vector Bundle
  • Short Exact Sequence
  • Homotopy Class
  • Obstruction Theory
  • Real Projective Space

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

partially supported by Max Planck Gesellschaft

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© 1988 Springer-Verlag

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Kaiser, U., Li, B.H. (1988). Enumeration of immersions of m-manifolds in (2m-2)-manifolds by the singularity method. In: Koschorke, U. (eds) Differential Topology. Lecture Notes in Mathematics, vol 1350. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081475

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  • DOI: https://doi.org/10.1007/BFb0081475

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  • Print ISBN: 978-3-540-50369-9

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