Groups of order 64 and non-homeomorphic double Kodaira fibrations with the same biregular invariants
Abstract
Abstract Let $$\Sigma _b$$ be a compact Riemann surface of genus b . We investigate finite quotients G of the pure braid group on two strands $$\textsf{P}_2(\Sigma _b)$$ which do not factor through $$\pi _1(\Sigma _b \times \Sigma _b)$$ . Building on our previous work on some special systems of generators on finite groups that we called diagonal double Kodaira structures , we prove that, if G does not have order 32, then $$|G| \ge 64$$ , and we completely classify the cases where $$b=2$$ and equality holds. In the last section, as a geometric application of our algebraic results, we construct two 3-dimensional families of double Kodaira fibrations having the same biregular invariants and the same Betti numbers but different fundamental group.
Fields of Study & Subjects
Finite Group Theory Research
Advanced Algebra and Geometry
Advanced Topics in Algebra
Publication details
- Journal / source
- Annali di Matematica Pura ed Applicata (1923 -)
- Publisher
- Springer Science and Business Media LLC
- Volume
- 205
- Issue
- 5
- Pages
- 2897-2922
- Publication date
- 17 April 2026
- Language
- EN