Skip to content
DraconiticResearch
Search Sources API
189,105 studies31 sourcesUpdated 59 min ago
PreprintCC BY 4.0arXiv

Top coefficients of ADO invariants are Murasugi-sum multiplicative

  • Daniel López Neumann
  • Roland van der Veen
Open at sourcePDFDOICite

Abstract

The Akutsu-Deguchi-Ohtsuki (ADO) invariants of links are a non-semisimple version of the colored Jones polynomials. We prove that the top coefficients of the ADO invariants of links in S3 are multiplicative under Murasugi-sum along connected minimal genus Seifert surfaces. More generally, for any simple complex Lie algebra g of type ADE and any r≥ 3, we prove that the top coefficient of the r-th g-ADO invariant is multiplicative under Murasugi-sum. As a corollary, we get that all the g-ADO invariants of fibred links are q-monic, generalizing a previous result of the authors for sl2. Moreover, whenever uq(g) is ribbon, we find an expression for the top coefficient of the r-th g-ADO invariant in terms of Hopf algebra integrals of universal uq(g)-invariants of bottom tangles.

Related

  1. The top coefficient of the Links-Gould invariant is Murasugi-sum multiplicative
    Cristina Anghel, Daniel López Neumann, Roland van der Veen
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryGeometry & topologyarXiv
  2. Logarithmic exponential sums with multiplicative coefficients
    Haozhe Gou
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Moments of random multiplicative functions with polynomial coefficients
    Xinyu Wang
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. On exponential sums with multiplicative coefficients
    Haozhe Gou
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. Effective estimates for exponential sums with multiplicative coefficients
    Nicolas Robles
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{neumann2026coefficients,
  title = {{Top coefficients of ADO invariants are Murasugi-sum multiplicative}},
  author = {Daniel López Neumann and Roland van der Veen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08638},
  eprint = {2610.08638},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08638},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Top coefficients of ADO invariants are Murasugi-sum multiplicative
AU  - Daniel López Neumann
AU  - Roland van der Veen
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08638
UR  - https://arxiv.org/abs/2610.08638
AB  - The Akutsu-Deguchi-Ohtsuki (ADO) invariants of links are a non-semisimple version of the colored Jones polynomials. We prove that the top coefficients of the ADO invariants of links in S^3 are multiplicative under Murasugi-sum along connected minimal genus Seifert surfaces. More generally, for any simple complex Lie algebra g of type ADE and any r≥ 3, we prove that the top coefficient of the r-th g-ADO invariant is multiplicative under Murasugi-sum. As a corollary, we get that all the g-ADO invariants of fibred links are q-monic, generalizing a previous result of the authors for sl_2. Moreover, whenever u_q(g) is ribbon, we find an expression for the top coefficient of the r-th g-ADO invariant in terms of Hopf algebra integrals of universal u_q(g)-invariants of bottom tangles.
ER  -