You are here: Seminars > 2025 > December 23rd
SUSTech
Time: 16:00-17:00 (GMT+8), Wednesday December 24th, 2025
Location: Zoom
Abstract:
In this report, we will give a classification of all regular maps \(\mathcal{M}\) on nonorientable surfaces with Euler
characteristic \(−p^3\) for some prime \(p ≥ 5\). Explicitly, it is proved that either \(\mathcal{M}\) has type \(\{4, m\}\) and
Aut\((\mathcal{M}) \cong (\mathbb{Z}_2 × \mathbb{Z}_2) ⋊ \mathbb{D}_{2m}\), where \(m \equiv 3 \pmod{6}\) and \(m−4 = p^3\); or \(\mathcal{M}\) has type \(\{2m, 2n\}\)
and Aut\((\mathcal{M}) \cong \mathbb{D}_{2m} × \mathbb{D}_{2n}\), where \(1 < m < n \), \(2 ∤ m\), \( \gcd(m, n) = 1\) and \(mn − m − n = p^3\). In particular,
there exists no such map provided \(p ≡ 1\pmod{12}\). Based on the currently available results, we also propose two
questions for further research. This is a joint work with Yao Tian.
Host: 甘芸松 Ganyun Song