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- W4289603208 abstract "We study some special systems of generators on finite groups, introduced in previous work by the first author and called diagonal double Kodaira structures, in order to investigate non-abelian, finite quotients of the pure braid group on two strands $mathsf{P}_2(Sigma_b)$, where $Sigma_b$ is a closed Riemann surface of genus $b$. In particular, we prove that, if a finite group $G$ admits a diagonal double Kodaira structure, then $|G|geq 32$, and equality holds if and only if $G$ is extra-special. In the last section, as a geometrical application of our algebraic results, we construct two $3$-dimensional families of double Kodaira fibrations having signature $16$. Such surfaces are different from the ones recently constructed by Lee, Lonne and Rollenske and, as far as we know, they provide the first examples of positive-dimensional families of double Kodaira fibrations with small signature." @default.
- W4289603208 created "2022-08-03" @default.
- W4289603208 creator A5080234571 @default.
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- W4289603208 date "2021-02-09" @default.
- W4289603208 modified "2023-09-28" @default.
- W4289603208 title "Extra-special quotients of surface braid groups and double Kodaira fibrations with small signature" @default.
- W4289603208 doi "https://doi.org/10.48550/arxiv.2102.04963" @default.
- W4289603208 hasPublicationYear "2021" @default.
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