Skip to content
DraconiticResearch
Search Sources API
210,095 studies31 sourcesUpdated 49 min ago
PreprintCC BY 4.0arXiv

On the Volume Conjectures for Dehn-filled $3$-manifolds along fundamental shadow link complements with big volume

  • Yunpeng Meng
  • Baojun Wu
  • Tian Yang
  • Yuxuan Yang
Open at sourcePDFDOICite

Abstract

We prove the Volume Conjecture and the Asymptotic Expansion Conjecture for closed oriented hyperbolic $3$-manifolds obtained by integral Dehn-fillings along a fundamental shadow link complement, provided that their volumes are sufficiently close to that of the complement. More generally, we show that the conjectured asymptotic expansions hold for pairs obtained by change-of-pair operations on a fundamental shadow link complement whenever the volume of the corresponding hyperbolic cone manifold is sufficiently close to that of the complement. A key ingredient in the proof is the introduction of extended quantum 6j-symbols and a Weak Reflection Symmetry satisfied by them. The Weak Reflection Symmetry is established by relating the extended quantum 6j-symbols to the b-6j symbols through a real Gevrey-$1$ estimate and a truncated Borel-Laplace transform.

Related

  1. Fundamental groups of complements of wobbly divisors in intersections of two quadrics
    Shomrik Bhattacharya, Yuki Matsubara
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. The second closed geodesic on Finsler manifolds with ℤ2 fundamental group
    Huagui Duan, Hui Liu, Wei Wang
    arXivPreprintarXiv licenceFull textDynamical systemsGeometry & topologyarXiv
  3. Simple homotopy types of smooth four-manifolds with finite fundamental group
    Daniel Kasprowski, John Nicholson
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  4. Finiteness of fundamental groups for manifolds with sign-changing Ricci curvature
    Lang Qin
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  5. Ricci-pinched 3-Manifolds with second-fundamental-form-pinched Boundary
    Chao Xia, Jincong Zheng
    arXivPreprintarXiv licenceFull textAnalysis & PDEsGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{meng2026volume,
  title = {{On the Volume Conjectures for Dehn-filled $3$-manifolds along fundamental shadow link complements with big volume}},
  author = {Yunpeng Meng and Baojun Wu and Tian Yang and Yuxuan Yang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.08517},
  eprint = {2611.08517},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.08517},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the Volume Conjectures for Dehn-filled $3$-manifolds along fundamental shadow link complements with big volume
AU  - Yunpeng Meng
AU  - Baojun Wu
AU  - Tian Yang
AU  - Yuxuan Yang
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.08517
UR  - https://arxiv.org/abs/2611.08517
AB  - We prove the Volume Conjecture and the Asymptotic Expansion Conjecture for closed oriented hyperbolic $3$-manifolds obtained by integral Dehn-fillings along a fundamental shadow link complement, provided that their volumes are sufficiently close to that of the complement. More generally, we show that the conjectured asymptotic expansions hold for pairs obtained by change-of-pair operations on a fundamental shadow link complement whenever the volume of the corresponding hyperbolic cone manifold is sufficiently close to that of the complement. A key ingredient in the proof is the introduction of extended quantum 6j-symbols and a Weak Reflection Symmetry satisfied by them. The Weak Reflection Symmetry is established by relating the extended quantum 6j-symbols to the b-6j symbols through a real Gevrey-$1$ estimate and a truncated Borel-Laplace transform.
ER  -