Pith. sign in

REVIEW

A cell decomposition for marked cycle curves

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 2410.21049 v1 pith:PPN4PIUJ submitted 2024-10-28 math.DS

Caroline Davis , Malavika Mukundan , Danny Stoll , Giulio Tiozzo This is my paper
classification math.DS
keywords cyclefamilycurvesmarkedtextrmcelldecompositionmathcal
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We describe a family $\textrm{Cyc}_p(\mathcal{F})$ of marked cycle curves that parameterize the cycles of period $p$ of a given family $\mathcal{F}$ of dynamical systems. We produce algorithms to compute a canonical cell decomposition for the marked cycle curves over the family $\textrm{Per}_1(0)$ of quadratic polynomials as well as over the family $\textrm{Per}_2(0)$ of quadratic rational maps with a critical 2-cycle. We obtain formulas for the number of $d$-cells in these decompositions, giving rise to e.g. a formula for their genus.

Discussion (0). Sign in to comment.

Pith tools