Pith. sign in

REVIEW 1 cited by

Essential annuli in genus two handlebody exteriors

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 2404.04503 v1 pith:VMQCIL62 submitted 2024-04-06 math.GT

Yuya Koda , Makoto Ozawa , Yi-Sheng Wang This is my paper · ORCID
classification math.GT
keywords annuliessentialclassificationexteriorgenushandlebodyexteriorsjsj-graph
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We classify all potential configurations of essential annuli in a genus two atoroidal handlebody exterior in the $3$-sphere, building on two recent classifications: the classification of the JSJ-graph of the exterior and the classification of essential annuli in the exterior. In contrast to knots, genus two handlebody exteriors may contain infinitely many non-isotopic essential annuli, due to the JSJ-graph classification. Our main result characterizes the numbers of different types of essential annuli in such an infinite family.

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. On symmetry and exterior problems of knotted handlebodies

    math.GT 2025-06 conditional novelty 7.0 of 10

    For handlebody-knots with type 4-1 annuli, the symmetry group is Z2 or Z2 x Z2, and the exterior determines the handlebody-knot up to isotopy via annulus slopes.

Pith tools