Knots whose braided satellite have the same HOMFLY polynomial up to given $z$-degrees

Tetsuya Ito

Knots whose braided satellite have the same HOMFLY polynomial up to given $z$-degrees

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 2410.12344 v2 pith:O62WLU34 submitted 2024-10-16 math.GT

Tetsuya Ito This is my paper · ORCID

classification math.GT

keywords givenbraideddegreeshomflyknotspolynomialsameconstruct

verification ladder T0 review T1 audit T2 compute T3 formal

0 comments

abstract

For a given knot $K$ and $w>0$, we construct infinitely many mutually distinct hyperbolic knots $\{K_i\}$ such that the $P$-satellites of $K$ and $K_i$ have the same HOMFLY polynomial up to given $z$-degrees, for all braided patterns $P$ with winding number less than or equal to $w$.

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

Bipartite expansion beyond biparticity
hep-th 2025-01 conditional novelty 6.0 of 10

The authors construct positive decompositions of fundamental HOMFLY polynomials in variables φ, φ̄, D for arbitrary knots, not just bipartite ones, and give a criterion to detect when such a decomposition conceals a b...

Pith tools