The Classification of Immersions of Spheres in Euclidean Spaces

  title={The Classification of Immersions of Spheres in Euclidean Spaces},
  author={Stephen Smale},
  journal={Annals of Mathematics},
  • S. Smale
  • Published 1 March 1959
  • Mathematics
  • Annals of Mathematics

Immersions of spheres and algebraically constructible functions

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We briefly review selected contributions to immersion-theoretic topology, from S. Smale's immersion theory for spheres to M. Gromov's convex integration theory, during the early "golden" period from

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A geometric classification of immersions of 3-manifolds into 5-space

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A (positive) locally convex curve in the 2-sphere is a curve with positive geodesic curvature (i.e., which always turns left). In the 3-sphere, it is a curve with positive torsion. In this work we



On the immersion ofn-manifolds in (n+1)-space

Regular curves on R k m a n n i a n manifolds

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CHERN, L a ge'ome'tric des sous-varie'te's d ' u n espace euclidean a p luskrs dimensions

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  • 1955

HIRSCH, O n immersions and regular homotopies of diferentiable manifolds, Abstract

  • Amer. Math. Soc.,
  • 1958

PAECHTER, The groups

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  • 1956