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Algebraic Vector Fields on S2 are $2$-generated

  • Yiyang Jiang
  • Xudong Chen
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Abstract

We exhibit two vector fields on S2, which generate the entire Lie algebra of algebraic vector fields. Compositions of the flows associated with these two vector fields enable us to approximate every diffeomorphism of S2 isotopic to the identity in the Cr-sense for any r≥ 0.

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Cite

BibTeXRIS
BibTeX
@misc{jiang2026algebraic,
  title = {{Algebraic Vector Fields on $S^2$ are $2$-generated}},
  author = {Yiyang Jiang and Xudong Chen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.36256},
  eprint = {2609.36256},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.36256},
}
RIS
TY  - UNPB
TI  - Algebraic Vector Fields on S^2 are $2$-generated
AU  - Yiyang Jiang
AU  - Xudong Chen
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.36256
UR  - https://arxiv.org/abs/2609.36256
AB  - We exhibit two vector fields on S^2, which generate the entire Lie algebra of algebraic vector fields. Compositions of the flows associated with these two vector fields enable us to approximate every diffeomorphism of S^2 isotopic to the identity in the C^r-sense for any r≥ 0.
ER  -