Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 52 min ago
PreprintarXiv licencearXiv

Weak reducibility for bridge trisections

  • Samuel Lewis-Monkman
Open at sourcePDFDOICite

Abstract

A bridge splitting of a knot is weakly reducible if it has a pair of disjoint shadows, one from above and one from below, in the splitting surface. The process of weak reduction exchanges local minima and maxima in the splitting, untelescoping the splitting and giving a method for detecting essential surfaces in the knot complement. Bridge trisections generalize bridge splittings to the setting of surfaces in 4-manifolds. We define weak reducibility in this context, giving diagrammatic conditions for carrying out a weak reduction operation on bridge splittings. We produce a partial classification of 4-bridge trisections of surfaces in S4.

Related

  1. Cantor Spectrum via a Reducibility-Duality Bridge for the Mosaic Almost Mathieu Operator
    Jiawei He, Yuan Shan, Yongjian Wang
    arXivPreprintarXiv licenceFull textDynamical systemsMathematical physicsarXiv
  2. Reducibility of linear representations, free ideals, and Kippenhahn's conjecture
    Michael Stessin, Rongwei Yang
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryAnalysis & PDEsarXiv
  3. Reducibility and Diagonal Equality Strata for Finite Jacobi Pencils
    Matthew Faust
    arXivPreprintarXiv licenceFull textAlgebra & number theoryAnalysis & PDEsarXiv
  4. Reducibility of symmetry on q-Painlevé equations
    Chihiro Sato, Kouichi Takemura, Ohka Yamashita
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  5. Martin-Löf randomness and rK-reducibility
    George Barmpalias, Lu Liu
    arXivPreprintarXiv licenceFull textLogic & foundationsarXiv

Cite

BibTeXRIS
BibTeX
@misc{lewismonkman2026weak,
  title = {{Weak reducibility for bridge trisections}},
  author = {Samuel Lewis-Monkman},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27382},
  eprint = {2610.27382},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27382},
}
RIS
TY  - UNPB
TI  - Weak reducibility for bridge trisections
AU  - Samuel Lewis-Monkman
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.27382
UR  - https://arxiv.org/abs/2610.27382
AB  - A bridge splitting of a knot is weakly reducible if it has a pair of disjoint shadows, one from above and one from below, in the splitting surface. The process of weak reduction exchanges local minima and maxima in the splitting, untelescoping the splitting and giving a method for detecting essential surfaces in the knot complement. Bridge trisections generalize bridge splittings to the setting of surfaces in 4-manifolds. We define weak reducibility in this context, giving diagrammatic conditions for carrying out a weak reduction operation on bridge splittings. We produce a partial classification of 4-bridge trisections of surfaces in S^4.
ER  -