The non-finite presentability of IA ( F 3 ) and GL 2 (Z[ t, t −1 ])

Krstić, Sava; McCool, James

doi:10.1007/s002220050174

Cited by 43 publications

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“…For n = 3, Krstić and McCool [31] showed that IA 3 is not finitely presentable. For n ≥ 4, it is also not known whether IA n is finitely presentable or not.…”

Section: Free Lie Algebras and Their Derivationsmentioning

confidence: 99%

A survey of the Johnson homomorphisms of the automorphism groups of free groups and related topics

Satoh

2016

IRMA Lectures in Mathematics and Theoretical Physics

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“…For n = 3, Krstić and McCool [31] showed that IA 3 is not finitely presentable. For n ≥ 4, it is also not known whether IA n is finitely presentable or not.…”

Section: Free Lie Algebras and Their Derivationsmentioning

confidence: 99%

A survey of the Johnson homomorphisms of the automorphism groups of free groups and related topics

Satoh

2016

IRMA Lectures in Mathematics and Theoretical Physics

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“…The Krstić-McCool result that T 3 is not finitely presented was proven in 1997, via completely algebraic methods [7]. It is a general fact that if the second homology of a group is not finitely generated, then the group is not finitely presented.…”

Section: Introductionmentioning

confidence: 99%

Dimension of the Torelli group for Out(Fn)

2007

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Abstract. Let Tn be the kernel of the natural map Out(Fn) → GLn(Z). We use combinatorial Morse theory to prove that Tn has an Eilenberg-MacLane space which is (2n − 4)-dimensional and that H 2n−4 (Tn, Z) is not finitely generated (n ≥ 3). In particular, this recovers the result of Krstić-McCool that T 3 is not finitely presented. We also give a new proof of the fact, due to Magnus, that Tn is finitely generated.

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“…For n = 3, Krstić and McCool [11] showed that IA 3 is not finitely presentable. For n ≥ 4, it is not known whether IA n is finitely presentable or not.…”

Section: Ia-automorphism Groupmentioning

confidence: 99%

The Johnson filtration of the McCool stabilizer subgroup of the automorphism group of a free group

Satoh

2011

Proc. Amer. Math. Soc.

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Abstract. Let F n be a free group of rank n with basis x 1 , x 2 , . . . , x n . We denote by S n the subgroup of the automorphism group of F n consisting of automorphisms which fix each of x 2 , . . . , x n and call it the McCool stabilizer subgroup. Let IS n be a subgroup of S n consisting of automorphisms which induce the identity on the abelianization of F n . In this paper, we determine the group structure of the lower central series of IS n and its graded quotients. Then we show that the Johnson filtration of S n coincides with the lower central series of IS n .

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The non-finite presentability of IA ( F 3 ) and GL 2 (Z[ t, t −1 ])

Cited by 43 publications

References 0 publications

A survey of the Johnson homomorphisms of the automorphism groups of free groups and related topics

A survey of the Johnson homomorphisms of the automorphism groups of free groups and related topics

Dimension of the Torelli group for Out(Fn)

The Johnson filtration of the McCool stabilizer subgroup of the automorphism group of a free group

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