A proof of the Chern-Lashof conjecture in dimensions greater than five

  title={A proof of the Chern-Lashof conjecture in dimensions greater than five},
  author={Richard Sharpe},
  journal={Commentarii Mathematici Helvetici},
  • R. Sharpe
  • Published 1 December 1989
  • Mathematics
  • Commentarii Mathematici Helvetici
SummaryChern and Lashof ([1], [2]) conjectured that if a smooth manifoldMm has an immersion intoRw, then the best possible lower bound for its total absolute curvature is the Morse number μ(M). We give a proof of this whenm>5. Under the same dimension restriction, our methods allow us to show that μ(M) is still the best possible lower bound among immersions within a fixed regular homotopy class except in the casew=m+1=even, for which the best lower bound is max {μ(M), 2 |d|}, whered the degree… 

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