Generating the Johnson filtration
نویسندگان
چکیده
منابع مشابه
Generating the Johnson filtration
For k ≥ 1, let I g (k) be the k term in the Johnson filtration of the mapping class group of a genus g surface with one boundary component. We prove that for all k ≥ 1, there exists some Gk ≥ 0 such that I g (k) is generated by elements which are supported on subsurfaces whose genus is at most Gk. We also prove similar theorems for the Johnson filtration of Aut(Fn) and for certain mod-p analogu...
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Answering a question of Farb–Leininger–Margalit, we give explicit lower bounds for the dilatations of pseudo-Anosov mapping classes lying in the kth term of the Johnson filtration of the mapping class group.
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The mapping class group of an oriented surface Σg,1 of genus g with one boundary component has a natural decreasing filtration Mg,1 ⊃ Mg,1(1) ⊃ Mg,1(2) ⊃ Mg,1(3) ⊃ · · · , where Mg,1(k) is the kernel of the action of Mg,1 on the kth nilpotent quotient of π1(Σg,1). Using a tree Lie algebra approximating the graded Lie algebra ⊕ k Mg,1(k)/Mg,1(k + 1) we prove that any integral homology sphere of ...
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ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2015
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2015.19.2217