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Morse relations for curvature and tightness

Part of the Lecture Notes in Mathematics book series (LNM,volume 209)

Abstract

In chapter I we define the oritical points of a continuous function ϕ: X → IR on a compact metric space X, and the Morse polynomial for an isolated critical point. We reproduce the proof of the Morse relations for a function with isolated critical points for this more general set-up. In chapter II we define polynomial, absolute and alternating curvature measures of certain maps or embeddings of X into EN in terms of critical points and we obtain Morse relations for these curvature measures. In chapter III we discuss maps (and sets) in EN of minimal total absolute curvature (tight maps) and we recall some results on tight embeddings of smooth, piecewise linear and topological manifolds.

Keywords

  • Simplicial Complex
  • Curvature Measure
  • Topological Manifold
  • Total Multiplicity
  • Real Projective Plane

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.

This is a considerably extended version of one of a series of four lectures given at the Liverpool Summer School on Singularities, June 1970.

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References

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© 1971 Springer-Verlag Berlin · Heidelberg

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Kuiper, N.H. (1971). Morse relations for curvature and tightness. In: Wall, C.T.C. (eds) Proceedings of Liverpool Singularities Symposium II. Lecture Notes in Mathematics, vol 209. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068893

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  • DOI: https://doi.org/10.1007/BFb0068893

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05511-2

  • Online ISBN: 978-3-540-36868-7

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