ar X iv : m at h / 05 01 05 1 v 1 [ m at h . G R ] 4 J an 2 00 5 INJECTIONS OF ARTIN GROUPS
نویسنده
چکیده
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.
منابع مشابه
ar X iv : m at h / 05 01 05 1 v 2 [ m at h . G R ] 1 7 M ay 2 00 6 INJECTIONS OF ARTIN GROUPS
We study those Artin groups which, modulo their centers, are finite index subgroups of the mapping class group of a sphere with at least 5 punctures. In particular, we show that any injective homomorphism between these groups is parameterized by a homeomorphism of a punctured sphere together with a map to the integers. We also give a generating set for the automorphism group of the pure braid g...
متن کاملar X iv : m at h / 04 01 05 6 v 1 [ m at h . G T ] 7 J an 2 00 4 SQUARE - TILED SURFACES IN H ( 2 )
This is a study of square-tiled translation surfaces in the stratum H(2) and their SL(2, R)-orbits or Teichmüller discs, which are arithmetic. We prove that for prime n > 3 translation surfaces tiled by n squares fall into two Teichmüller discs, only one of them with elliptic points, and that the genus of these discs has a cubic growth rate in n.
متن کاملar X iv : m at h / 05 05 01 1 v 4 [ m at h . PR ] 5 J un 2 00 6 EXCHANGEABLE , GIBBS AND EQUILIBRIUM MEASURES FOR MARKOV
We study a class of strongly irreducible, multidimensional, topological Markov shifts, comparing two notions of “symmetric measure”: exchangeability and the Gibbs (or conformal) property. We show that equilibrium measures for such shifts (unique and weak Bernoulli in the one dimensional case) exhibit a variety of spectral properties.
متن کامل