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High-dimensional knots corresponding to the fractional Fibonacci groups

Andrzej Szczepański, Andreĭ Vesnin (1999)

Fundamenta Mathematicae

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.

Homomorphic extensions of Johnson homomorphisms via Fox calculus

Bernard Perron (2004)

Annales de l’institut Fourier

Using Fox differential calculus, for any positive integer k , we construct a map on the mapping class group g , 1 of a surface of genus g with one boundary component, such that, when restricted to an appropriate subgroup, it coincides with the k + 1 t h Johnson-Morita homomorphism. This allows us to construct very easily a homomorphic extension to g , 1 of the second and third Johnson-Morita homomorphisms.

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