Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 55 min ago
PreprintCC BY-NC-SA 4.0arXiv

Splitting spheres for S2-links in S4

  • Jianfeng Lin
  • Yi Xie
  • Boyu Zhang
Open at sourcePDFDOICite

Abstract

We prove that every smooth two-component split sphere link Lsqcup R⊂ S4 admits infinitely many smooth splitting $3$-spheres that are topologically non-isotopic. This generalizes a theorem of Tatsuoka from the two-component sphere unlink to split links with arbitrarily knotted sphere components. In the course of the proof, we establish a general sufficient condition under which a connected sum of smooth $4$-manifolds admits infinitely many topologically non-isotopic splitting $3$-spheres. This criterion may be of independent interest; in particular, it applies to all previously known examples of nonuniqueness for splitting $3$-spheres of positive-genus surface links.

Related

  1. Homotopy groups of spheres and dimension quotients
    Laurent Bartholdi, Roman Mikhailov
    J. Top.Peer-reviewedLicence not statedFull text1 citedAlgebra & number theoryGeometry & topologyHAL
  2. Length spectrum rigidity and flexibility of spheres of revolution with one equator
    Alberto Abbondandolo, Marco Mazzucchelli
    HALPreprintPublisher termsFull textGeneral mathematicsHAL
  3. Fluid dynamic limit of Boltzmann equation for granular hard-spheres in a nearly elastic regime
    Ricardo J. Alonso, Bertrand Lods, Isabelle Tristani
    Mémoires de la Société mathématique de FrancePeer-reviewedLicence not statedFull text16 citedGeneral mathematicsOpenAlex
  4. Some homotopy coherent finite group actions on spheres
    Manuel Krannich, Oscar Randal-Williams
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  5. Diameter of quotients of spheres in spin modules and quantum control
    Jean-Paul Gauthier
    HALPreprintCC BY-NC 4.0Full textGeneral mathematicsHAL

Cite

BibTeXRIS
BibTeX
@misc{lin2026splitting,
  title = {{Splitting spheres for $S^2$-links in $S^4$}},
  author = {Jianfeng Lin and Yi Xie and Boyu Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.02785},
  eprint = {2608.02785},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.02785},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Splitting spheres for S^2-links in S^4
AU  - Jianfeng Lin
AU  - Yi Xie
AU  - Boyu Zhang
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2608.02785
UR  - https://arxiv.org/abs/2608.02785
AB  - We prove that every smooth two-component split sphere link Lsqcup R⊂ S^4 admits infinitely many smooth splitting $3$-spheres that are topologically non-isotopic. This generalizes a theorem of Tatsuoka from the two-component sphere unlink to split links with arbitrarily knotted sphere components. In the course of the proof, we establish a general sufficient condition under which a connected sum of smooth $4$-manifolds admits infinitely many topologically non-isotopic splitting $3$-spheres. This criterion may be of independent interest; in particular, it applies to all previously known examples of nonuniqueness for splitting $3$-spheres of positive-genus surface links.
ER  -