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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.
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