Finiteness properties for a subgroup of the pure symmetric automorphism group

Details Finiteness properties for a subgroup of the pure symmetric automorphism group Finiteness properties for a subgroup of the pure symmetric automorphism group

2006-02-08

arxiv.org/abs/math/0602148v2

Mathematics

Group Theory

Originally titled "Finiteness properties for the kernel of pure motions of n unlinked loops"; error in Lemma 3.2 removed; argu

Scientific paper

Let F_n be the free group on n generators, and P\Sigma_n be the group of automorphisms of F_n which send each generator to a conjugate of itself. Let K_n be the kernel of the homomorphism from P\Sigma_n to P\Sigma_{n-1} induced by mapping one of the free group generators to the identity. We show that K_n has cohomological dimension n-1, and that the ith cohomology groups are infinitely generated for all i between 2 and n-1. It follows that K_n is not finitely presentable for n>2.

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