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A small normal generating set for the handlebody subgroup of the Torelli group

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arxiv 1607.06553 v1 pith:CETBYSMF submitted 2016-07-22 math.GT math.GR

Genki Omori This is my paper · ORCID
classification math.GTmath.GR
keywords grouphandlebodysubgroupgeneratingnormalorientablesurfacetorelli
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abstract

We prove that the handlebody subgroup of the Torelli group of an orientable surface is generated by genus one BP-maps. As an application, we give a normal generating set for the handlebody subgroup of the level $d$ mapping class group of an orientable surface.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Birman--Craggs--Johnson homomorphism and the handlebody Torelli group

    math.GT 2026-07 conditional novelty 6.0 of 10

    For genus at least 3, the BCJ image of the handlebody Torelli group is an explicit monomial subspace B^bi_3, and of the Johnson kernel is B^bi_2; cup-product lower bounds of order g^6 and g^4 follow.

  2. Abelianizations of finite-index subgroups of the handlebody group

    math.GT 2026-07 accept novelty 6.0 of 10

    For genus ≥ 4, meridian multitwists vanish in H_1 of any finite-index subgroup of the handlebody group, and subgroups containing the Torelli group, twist group, or Johnson kernel have trivial rational abelianization.

  3. Johnson homomorphisms and the second rational cohomology of handlebody Torelli groups

    math.GT 2025-09 conditional novelty 6.0 of 10

    For the handlebody Torelli groups HI and HBI, the kernels of the Johnson-detected cup product maps in second rational cohomology are computed explicitly as sums of irreducible SL_g(Q) modules.

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