Pith. sign in

REVIEW 1 cited by

The second Johnson homomorphism and the second rational cohomology of the Johnson kernel

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv math/0601314 v2 pith:5U3FELEQ submitted 2006-01-13 math.GT

Takuya Sakasai This is my paper · ORCID
classification math.GT
keywords johnsonsecondhomomorphismkernelrationalcohomologygroupabelian
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

The Johnson kernel is the subgroup of the mapping class group of a surface generated by Dehn twists along bounding simple closed curves, and has the second Johnson homomorphism as a free abelian quotient. In terms of the representation theory of the symplectic group, we give a complete description of cup products of two classes in the first rational cohomology of the Johnson kernel obtained by the rational dual of the second Johnson homomorphism.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. 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.

Pith tools