Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 20 min ago
PreprintarXiv licencearXiv

Quantum Invariants indexed by Fibered Faces of the Thurston Polytope

  • Davide Passaro
  • Lara San Martín Suárez
Open at sourcePDFDOICite

Abstract

We study the Gukov--Manolescu quantum invariant for oriented links. While this invariant is a single series in the knot case, we find that links admit multiple such series, each one consistent with the Melvin--Morton--Rozansky expansion of the colored Jones polynomials. We prove that convergent inverted state sums yield a family of multivariable Gukov--Manolescu series, indexed by monomials of the Alexander polynomial. We conjecture that these monomials correspond precisely to the fibered faces of the Thurston norm ball and provide extensive computational evidence for this correspondence. Further results concerning the leading term, the corresponding single-variable invariant, and the effect of partial Dehn surgery are also established.

Related

  1. Cannon-Thurston Maps, Harmonic Maps, and Minimal Surfaces in Fibered Hyperbolic 3-Manifolds
    Alberto Verjovsky
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  2. Computation of leading coefficients in asymptotics of relative quantum invariants
    Ka Ho Wong, Tian Yang
    Advances in MathematicsPeer-reviewedLicence not statedFull text11 citedGeometry & topologyOpenAlex
  3. Two non-semisimple quantum invariants of lens spaces
    Rhea Palak Bakshi, Mitchell Jubeir, Quinn T. Kolt
    arXivPreprintarXiv licenceFull textAlgebra & number theoryGeometry & topologyarXiv
  4. Analytic quantum invariants
    Rinat Kashaev, Vladimir Mangazeev, Marcos Marino
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryGeometry & topologyarXiv
  5. Clifford Invariants and Three-Copy Quantum Tests
    Xingya Fan, Yongzhi Luan
    arXivPreprintarXiv licenceFull textAlgebra & number theoryQuantum physics & quantum informationarXiv

Cite

BibTeXRIS
BibTeX
@misc{passaro2026quantum,
  title = {{Quantum Invariants indexed by Fibered Faces of the Thurston Polytope}},
  author = {Davide Passaro and Lara San Martín Suárez},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12311},
  eprint = {2609.12311},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12311},
}
RIS
TY  - UNPB
TI  - Quantum Invariants indexed by Fibered Faces of the Thurston Polytope
AU  - Davide Passaro
AU  - Lara San Martín Suárez
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.12311
UR  - https://arxiv.org/abs/2609.12311
AB  - We study the Gukov--Manolescu quantum invariant for oriented links. While this invariant is a single series in the knot case, we find that links admit multiple such series, each one consistent with the Melvin--Morton--Rozansky expansion of the colored Jones polynomials. We prove that convergent inverted state sums yield a family of multivariable Gukov--Manolescu series, indexed by monomials of the Alexander polynomial. We conjecture that these monomials correspond precisely to the fibered faces of the Thurston norm ball and provide extensive computational evidence for this correspondence. Further results concerning the leading term, the corresponding single-variable invariant, and the effect of partial Dehn surgery are also established.
ER  -