Torus Surgery Constraints and Intermediate Covers of the Cartwright--Steger Surface

@misc{akhmedov2026torus,
  title = {{Torus Surgery Constraints and Intermediate Covers of the Cartwright--Steger Surface}},
  author = {Anar Akhmedov and Sai-Kee Yeung},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06442},
  eprint = {2610.06442},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.06442},
}

TY  - UNPB
TI  - Torus Surgery Constraints and Intermediate Covers of the Cartwright--Steger Surface
AU  - Anar Akhmedov
AU  - Sai-Kee Yeung
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.06442
UR  - https://arxiv.org/abs/2610.06442
AB  - We study torus surgery on the Cartwright--Steger surface and the degree-two cover construction proposed in \cite[Remark~1]{ASY}. Every torus in this surface is integrally nullhomologous, and surgery on a fixed disjoint collection of such tori cannot decrease the first Betti number. We then determine the nodal-curve subgroup and complete the fundamental-group calculation in the degree-two construction. The resulting minimal symplectic manifold has signature zero and fundamental group Z/2; for compatible symplectic gluings, its universal cover is an exotic symplectic 31CP^2#31CP̅^ 2. The construction on the original Cartwright--Steger surface gives a minimal symplectic manifold with signature −1 and fundamental group (Z/2)^2.
ER  -