Pith. sign in

REVIEW 4 cited by

Surface Drinfeld Torsors I : Higher Genus Associators

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 2004.07303 v1 pith:FZMDJP2M submitted 2020-04-15 math.QA math.AT

Martin Gonzalez This is my paper · ORCID
classification math.QAmath.AT
keywords genushigherassociatorsdefineframedversiondrinfelddata
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We develop a higher genus version of Drinfeld associators by means of operad theory. We start by introducing a framed version of rational associators and Grothendieck-Teichm\"uller groups and show that their definition is independent of the framing data. Next, we define a framed version of the universal KZ connection and we use it to show that over the complex numbers, the rational framed Drinfeld torsor is not empty. Next, we concentrate on the higher genus version of this story. We define an operad module of framed parenthesized higher genus braidings in prounipotent groupoids and we define its chord diagram counterpart. We then use these operadic modules to operadicly define higher genus associators and Grothendieck-Teichm\"uller groups, which again do not depend on the framing data. Finally, we compare our results in the genus $1$ case with those appearing in the litterature.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 4 Pith papers

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

  1. The formality of the Goldman-Turaev Lie bialgebra on a closed surface

    math.QA 2025-02 accept novelty 8.0 of 10

    The pro-unipotent automorphism group of the associated graded Goldman-Turaev Lie bialgebra on a closed surface is explicitly described in terms of a divergence map and the kernel of a reduced coproduct.

  2. Degenerations of flat connections on Riemann surfaces

    hep-th 2026-07 accept novelty 7.0 of 10

    Enriquez and DHS kernels on genus-h surfaces close under non-separating degeneration to genus h-1 kernels with two punctures whose generators are Bernoulli series in the original Lie algebra elements.

  3. Higher-genus multiple zeta values

    hep-th 2025-07 conditional novelty 7.0 of 10

    The paper defines higher-genus multiple zeta values, regularizes them via Schottky uniformization, and proves and conjectures new identities among them.

  4. The framed version of the universal KZB connection in higher genera

    math.QA 2026-07 accept novelty 6.5 of 10

    A unique operadic framed lift of Enriquez' KZB connection exists on any marked closed Riemann surface and its monodromy yields a genus-g Gonzalez–Drinfeld associator.

Pith tools