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PreprintCC BY 4.0arXiv

Brieskorn spheres bound orbit spaces of torus manifolds

  • Grigory Solomadin
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Abstract

We construct a smooth, equivariantly formal, simply connected torus $8$-manifold over a contractible $4$-manifold with the boundary a Brieskorn homology $3$-sphere having a nontrivial fundamental group. We prove extension to a torus graph for GKM graphs of GKM4 manifolds in complexity $2$, and $3$ under a finite fundamental group assumption (that is not satisfied, in general).

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Cite

BibTeXRIS
BibTeX
@misc{solomadin2026brieskorn,
  title = {{Brieskorn spheres bound orbit spaces of torus manifolds}},
  author = {Grigory Solomadin},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30513},
  eprint = {2608.30513},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30513},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Brieskorn spheres bound orbit spaces of torus manifolds
AU  - Grigory Solomadin
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.30513
UR  - https://arxiv.org/abs/2608.30513
AB  - We construct a smooth, equivariantly formal, simply connected torus $8$-manifold over a contractible $4$-manifold with the boundary a Brieskorn homology $3$-sphere having a nontrivial fundamental group. We prove extension to a torus graph for GKM graphs of GKM_4 manifolds in complexity $2$, and $3$ under a finite fundamental group assumption (that is not satisfied, in general).
ER  -