We study several geometric and group theoretical problems related to Kodaira fibrations, more general families of Riemann surfaces, surface-by-surface groups. First we provide constraints on fibrations that fiber in than two distinct ways, addressing a question by Catanese Salter about their existence. Then show if the fundamental surface bundle over is ${\rm CAT}(0)$ group, must have injective...

We describe a simple locally CAT(0) classifying space for XXL type Artin groups (with all labels at least 5). Furthermore, when the group is not dihedral, we rank 1 periodic geodesic, thus proving that are acylindrically hyperbolic. Together with Property RD proved by Ciobanu, Holt and Rees, property implies Baum–Connes conjecture groups.

Abstract Using techniques in motivic homotopy theory, especially the theorem of Gheorghe, second and third author on isomorphism between Adams spectral sequence for $C\tau $ C τ algebraic Novikov $BP_{*}$ B P ∗ , we com...

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