The Real Albanese Map and Smooth Topology of the Cartwright--Steger Quotient

@misc{akhmedov2026real,
  title = {{The Real Albanese Map and Smooth Topology of the Cartwright--Steger Quotient}},
  author = {Anar Akhmedov and Sai-Kee Yeung},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04460},
  eprint = {2610.04460},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04460},
}

TY  - UNPB
TI  - The Real Albanese Map and Smooth Topology of the Cartwright--Steger Quotient
AU  - Anar Akhmedov
AU  - Sai-Kee Yeung
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2610.04460
UR  - https://arxiv.org/abs/2610.04460
AB  - Let X be the Cartwright--Steger surface with its real involution c and Albanese map α:X→ E, and put Y=X/⟨ c⟩. Every smooth real Albanese fiber has two ovals and is nondividing. The branch surface B≅#_3ℝℙ^2 satisfies j_*π_1(B)=4ℤ⊂π_1(Y)≅ℤ and is nullhomologous modulo two. Every smoothly embedded +1-sphere representing the positive generator of H_2(Y;ℤ) meets B in at least six points. Its lift has square two, pairs trivially with K_X, and has no connected embedded representative of genus zero or one. Circle surgery on an Albanese generator is homeomorphic to ℂℙ^2 for either normal framing. Blowing down a positive sphere, if one exists, gives a ℤ[ℤ]-homology S^1× S^3 homotopy equivalent to S^1× S^3.
ER  -