Hausdorff combing of groups and for universal covering spaces of closed 3-manifolds
We prove that the natural HNN-extensions of the fractional Fibonacci groups are the fundamental groups of high-dimensional knot complements. We also give some characterization and interpretation of these knots. In particular we show that some of them are 2-knots.
Using Fox differential calculus, for any positive integer , we construct a map on the mapping class group of a surface of genus with one boundary component, such that, when restricted to an appropriate subgroup, it coincides with the Johnson-Morita homomorphism. This allows us to construct very easily a homomorphic extension to of the second and third Johnson-Morita homomorphisms.