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Conformal curvature for the normal bundle of a conformal foliation

Angel Montesinos (1982)

Annales de l'institut Fourier

It is proved that the normal bundle of a distribution 𝒱 on a riemannian manifold admits a conformal curvature C if and only if 𝒱 is a conformal foliation. Then is conformally flat if and only if C vanishes. Also, the Pontrjagin classes of can be expressed in terms of C .

Conjugacy for positive permutation braids

Hugh R. Morton, Richard J. Hadji (2005)

Fundamenta Mathematicae

Positive permutation braids on n strings, which are defined to be positive n-braids where each pair of strings crosses at most once, form the elementary but non-trivial building blocks in many studies of conjugacy in the braid groups. We consider conjugacy among these elementary braids which close to knots, and show that those which close to the trivial knot or to the trefoil are all conjugate. All such n-braids with the maximum possible crossing number are also shown to be conjugate. ...

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