Publications et prépublications
en liaison avec les tresses
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| Abstract:
We consider the Artin groups of dihedral type $A_k=\langle a,b | prod(a, b; k)=prod(b, a; k)\rangle$ where $prod(s, t; k)=ststs...$ with $k$ terms in the product on the right-hand side. We prove that the spherical growth series and the geodesic growth series of $A_k$ with respect to the Artin generators
$\{a, b, a^{-1}, b^{-1}\}$ are rational. We provide explicit formulas for the series.
MSC : |
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| Abstract:
We study those Artin groups which, modulo their centers, are
finite index subgroups of the mapping class group of a punctured sphere.
In particular, we show that any injective homomorphism between these
groups is parameterized by a homeomorphism of a punctured disk together
with a homomorphism to the integers. The technique, following Ivanov, is
to prove that every superinjective map of the complex of curves of a
sphere with at least 5 punctures is induced by a homeomorphism.
MSC : 20F36, 57M07 |
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