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Some non-trivial PL knots whose complements are homotopy circles

Greg Friedman (2007)

Fundamenta Mathematicae

We show that there exist non-trivial piecewise linear (PL) knots with isolated singularities S n - 2 S , n ≥ 5, whose complements have the homotopy type of a circle. This is in contrast to the case of smooth, PL locally flat, and topological locally flat knots, for which it is known that if the complement has the homotopy type of a circle, then the knot is trivial.

Some remarks on Koszul algebras and quantum groups

Yu. I. Manin (1987)

Annales de l'institut Fourier

The category of quadratic algebras is endowed with a tensor structure. This allows us to construct a class of Hopf algebras studied recently under the name of quantum (semi) groups.

Some remarks on Lie flows.

Miquel Llabrés, Agustí Reventós (1989)

Publicacions Matemàtiques

The first part of this paper is concerned with geometrical and cohomological properties of Lie flows on compact manifolds. Relations between these properties and the Euler class of the flow are given.The second part deals with 3-codimensional Lie flows. Using the classification of 3-dimensional Lie algebras we give cohomological obstructions for a compact manifold admits a Lie flow transversely modeled on a given Lie algebra.

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