Finite quotients G of P2(Σb) not factoring through π1(Σb×Σb) satisfy |G|≥64 (except order-32 cases), with complete classification at order 64; this yields two 3-dimensional families of non-homeomorphic double Kodaira fibrations with identical biregular invariants and Betti numbers.
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Groups of order 64 and non-homeomorphic double Kodaira fibrations with the same biregular invariants
Finite quotients G of P2(Σb) not factoring through π1(Σb×Σb) satisfy |G|≥64 (except order-32 cases), with complete classification at order 64; this yields two 3-dimensional families of non-homeomorphic double Kodaira fibrations with identical biregular invariants and Betti numbers.