On the d-invariants of Brieskorn spheres and GL(2,ℤ)

@misc{harichurn2026dinvariants,
  title = {{On the $d$-invariants of Brieskorn spheres and $\mathrmGL(2,\mathbbZ)$}},
  author = {Shimal Harichurn and Isabella Khan and András Némethi and Josef Svoboda},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36472},
  eprint = {2610.36472},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36472},
}

TY  - UNPB
TI  - On the d-invariants of Brieskorn spheres and GL(2,ℤ)
AU  - Shimal Harichurn
AU  - Isabella Khan
AU  - András Némethi
AU  - Josef Svoboda
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.36472
UR  - https://arxiv.org/abs/2610.36472
AB  - We study the d-invariant from Heegaard Floer homology for Brieskorn spheres Σ(p,q,r). Using surgeries on two singular fibers, we establish new relations of the d-invariants among various Brieskorn spheres. For p=2, we show that d never vanishes if q/r lies in certain intervals on the rational line. Altogether, we completely classify Brieskorn spheres Σ(2,q,r) with d=0. The zero set is expressed using submonoids of GL(2,ℤ) and the Stern--Brocot tree. As an application, we prove that most Brieskorn spheres Σ(2,q,r) do not bound a rational homology $4$-ball.
ER  -