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Gauge theory on Cohomogeneity One Spin(7)-Manifolds from Aloff--Wallach Spaces

  • Hanci Chi
  • Enric Solé-Farré
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Abstract

We begin a systematic study of Spin(7)-instantons on complete non-compact cohomogeneity one Spin(7)-manifolds with Aloff--Wallach spaces Nk,l=SU(3)/U(1)k,l as principal orbits. We provide a complete classification of admissible principal U(1)- and SO(3)-bundles and smooth bounded solutions to the Spin(7)-instanton equation on them. We study bubbling phenomena for the constructed Spin(7)-instantons and discuss the compactification of the moduli space of Spin(7)-instantons in both the ALC and AC settings.

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Cite

BibTeXRIS
BibTeX
@misc{chi2026gauge,
  title = {{Gauge theory on Cohomogeneity One Spin(7)-Manifolds from Aloff--Wallach Spaces}},
  author = {Hanci Chi and Enric Solé-Farré},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27686},
  eprint = {2610.27686},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27686},
}
RIS
TY  - UNPB
TI  - Gauge theory on Cohomogeneity One Spin(7)-Manifolds from Aloff--Wallach Spaces
AU  - Hanci Chi
AU  - Enric Solé-Farré
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.27686
UR  - https://arxiv.org/abs/2610.27686
AB  - We begin a systematic study of Spin(7)-instantons on complete non-compact cohomogeneity one Spin(7)-manifolds with Aloff--Wallach spaces N_k,l=SU(3)/U(1)_k,l as principal orbits. We provide a complete classification of admissible principal U(1)- and SO(3)-bundles and smooth bounded solutions to the Spin(7)-instanton equation on them. We study bubbling phenomena for the constructed Spin(7)-instantons and discuss the compactification of the moduli space of Spin(7)-instantons in both the ALC and AC settings.
ER  -