Pith. sign in

REVIEW 1 cited by

TG-Hyperbolicity of Virtual Links

Not yet reviewed by Pith; the record is open.

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 1904.06385 v1 pith:6L7M3LNI submitted 2019-04-12 math.GT

classification math.GT
keywords linksvirtualtg-hyperbolictg-hyperbolicitytheoryextendsurfacesvolumes
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

We extend the theory of hyperbolicity of links in the 3-sphere to tg-hyperbolicity of virtual links, using the fact that the theory of virtual links can be translated into the theory of links living in closed orientable thickened surfaces. When the boundary surfaces are taken to be totally geodesic, we obtain a tg-hyperbolic structure with a unique associated volume. We prove that all virtual alternating links are tg-hyperbolic. We further extend tg-hyperbolicity to several classes of non-alternating virtual links. We then consider bounds on volumes of virtual links and include a table for volumes of the 116 nontrivial virtual knots of four or fewer crossings, all of which, with the exception of the trefoil knot, turn out to be tg-hyperbolic.

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. The Jones-Krushkal polynomial and minimal diagrams of surface links

    math.GT 2019-08 conditional novelty 8.0 of 10

    Reduced alternating diagrams of links in thickened surfaces and of virtual links minimize crossing number, and any two such diagrams of the same link have the same writhe.

Pith tools