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1	A new filtration of the Magnus kernel McNeill, Reagin 16 September 2013 (has links) For a oriented genus g surface with one boundary component, S_g, the Torelli group is the group of orientation preserving homeomorphisms of S_g that induce the identity on homology. The Magnus representation of the Torelli group represents the action on F/F'' where F=π_1(S_g) and F'' is the second term of the derived series. I show that the kernel of the Magnus representation, Mag(S_g), is highly non-trivial and has a rich structure as a group. Specifically, I define an infinite filtration of Mag(S_g) by subgroups, called the higher order Magnus subgroups, M_k(S_g). I develop methods for generating nontrivial mapping classes in M_k(S_g) for all k and g≥2. I show that for each k the quotient M_k(S_g)/M_{k+1}(S_g) contains a subgroup isomorphic to a lower central series quotient of free groups E(g-1)_k/E(g-1)_{k+1}. Finally I show that for g≥3 the quotient M_k(S_g)/M_{k+1}(S_g) surjects onto an infinite rank torsion free abelian group. To do this, I define a Johnson-type homomorphism on each higher order Magnus subgroup quotient and show it has a highly non-trivial image. lower central series surfaces mapping class groups pure braids Magnus kernel free groups Johnson subgroups
2	Discrete and Profinite Groups Acting on Regular Rooted Trees / Diskrete und pro-endliche Gruppen, die auf regulären Bäumen mit einem Fixpunkt operieren Siegenthaler, Olivier 28 September 2009 (has links) No description available. 510 Mathematik ECAE 080 Mathematics and Natural Science Gruppen die auf Bäumen operieren selbstähnliche Gruppen Kranzprodukte pro-endliche Gruppen affine Gruppenschemata Zentralreihen Automorphismentürme Hausdorff Dimension Grigorchuk Gruppe Kongruenzprobleme groups acting on trees self-similar groups wreath products profinite groups affine group schemes central series automorphism towers Hausdorff dimension Grigorchuk group congruence problems 31.21

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A new filtration of the Magnus kernel

Discrete and Profinite Groups Acting on Regular Rooted Trees / Diskrete und pro-endliche Gruppen, die auf regulären Bäumen mit einem Fixpunkt operieren