Dimension of the Torelli group for Out(Fn)

Bestvina, Mladen; Bux, Kai Uwe; Margalit, Dan

doi:10.1007/s00222-007-0055-0

Cited by 34 publications

(71 citation statements)

References 16 publications

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“…The authors [3] recently proved that cd(I(S g )) < 4g − 5 = vcd(Mod(S g )). (Harer's result already implied that cd(I(S g )) ≤ 4g − 5.…”

Section: Theorem E the Complex B(s Gmentioning

confidence: 99%

“…In an earlier paper, the authors [3] studied the Torelli subgroup of Out(F n ), that is, the group T n of outer automorphisms of a free group of rank n that act trivially on the first homology of the free group. The main results of that paper (that cd(T n ) = 2n − 4 and that H 2n−4 (T n , Z) is infinitely generated) are analogous to Theorems A and C of the present paper.…”

Section: Theorem E the Complex B(s Gmentioning

confidence: 99%

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The dimension of the Torelli group

Bestvina

Bux

Margalit

2009

J. Amer. Math. Soc.

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We prove that the cohomological dimension of the Torelli group for a closed, connected, orientable surface of genus g ≥ 2 g \geq 2 is equal to 3 g − 5 3g-5 . This answers a question of Mess, who proved the lower bound and settled the case of g = 2 g=2 . We also find the cohomological dimension of the Johnson kernel (the subgroup of the Torelli group generated by Dehn twists about separating curves) to be 2 g − 3 2g-3 . For g ≥ 2 g \geq 2 , we prove that the top dimensional homology of the Torelli group is infinitely generated. Finally, we give a new proof of the theorem of Mess that gives a precise description of the Torelli group in genus 2. The main tool is a new contractible complex, called the “complex of minimizing cycles”, on which the Torelli group acts.

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“…The authors [3] recently proved that cd(I(S g )) < 4g − 5 = vcd(Mod(S g )). (Harer's result already implied that cd(I(S g )) ≤ 4g − 5.…”

Section: Theorem E the Complex B(s Gmentioning

confidence: 99%

Section: Theorem E the Complex B(s Gmentioning

confidence: 99%

The dimension of the Torelli group

Bestvina

Bux

Margalit

2009

J. Amer. Math. Soc.

Self Cite

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“…Furthermore, if i l > i then by using the above equation and part (6) of Lemma 4·5, we see This shows that we may assume i 1 · · · i l in (4·1).…”

Section: Takao Satohmentioning

confidence: 83%

On the basis-conjugating automorphism groups of free groups and free metabelian groups

Satoh

2014

Math. Proc. Camb. Phil. Soc.

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In this paper we study the images of the Johnson homomorphisms of the basis-conjugating automorphism groups of free groups and free metabelian groups. In particular, we show that the Johnson image is contained in a certain proper Lie subalgebra p M n of the derivation algebra of the Chen Lie algebra. Furthermore, we completely determine the Johnson images, and give the abelianisation of p M n as a Lie algebra by using Morita's trace maps.

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“…Automorphisms of free groups have been widely studied over the years, from many different points of view. They are linked to the mapping class groups of surfaces and braid groups [FM12a]; they also act on a moduli space of graphs, called the outer space, introduced in [CV86], which is still actively studied nowadays (see, for instance, [BBM07], or [FM12b]). Recently, several results have also been obtained regarding the stable homology of these groups [Gal11,RWW17,DV15,Dja16a].…”

Section: Introductionmentioning

confidence: 99%

“…We then put aside this linear part by considering only IA n , the subgroup of automorphisms acting trivially on Z n , which is an algebraic analogue of the Torelli subgroup of the mapping class group. An explicit finite set of generators of IA n has been known for a long time [Nie24] -see also [BBM07,5.6]. Nevertheless, the structure of IA n remains largely mysterious.…”

Section: Introductionmentioning

confidence: 99%

On the stable Andreadakis problem

Darné

2019

Journal of Pure and Applied Algebra

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Let F n be the free group on n generators. Consider the group IA n of automorphisms of F n acting trivially on its abelianization. There are two canonical filtrations on IA n : the first one is its lower central series Γ * ; the second one is the Andreadakis filtration A * , defined from the action on F n . In this paper, we establish that the canonical morphism between the associated graded Lie rings L(Γ * ) and L(A * ) is stably surjective. We then investigate a p-restricted version of the Andreadakis problem. A calculation of the Lie algebra of the classical congruence group is also included. arXiv:1711.05991v2 [math.AT]

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Dimension of the Torelli group for Out(Fn)

Cited by 34 publications

References 16 publications

The dimension of the Torelli group

The dimension of the Torelli group

On the basis-conjugating automorphism groups of free groups and free metabelian groups

On the stable Andreadakis problem

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