Constructs closed and aspherical manifolds with vanishing L2-Betti numbers over every field whose fundamental groups are residually torsionfree and nilpotent yet do not virtually fibre over the circle, yielding counterexamples to weakening Kielak's theorem.
and Italiano, Giovanni and Kielak, Dawid , year =
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A PD^3 group with an unbounded quasimorphism whose quasikernel is coarsely connected is either a torus or Klein bottle bundle over a circle, or is quasiisometric to a curved (R^3,g) with hyperbolic-plane fibres.
Establishes Strong Atiyah Conjecture for finite-index torsion-free subgroups of Out(G) when G is a surface group, free group or RAAG, implying discrete von Neumann dimensions and Zero Divisor Conjecture for the group algebras.
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Some closed manifolds that do not fibre over the circle
Constructs closed and aspherical manifolds with vanishing L2-Betti numbers over every field whose fundamental groups are residually torsionfree and nilpotent yet do not virtually fibre over the circle, yielding counterexamples to weakening Kielak's theorem.
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Quasimorphisms and Poincar\'e duality in dimension 3
A PD^3 group with an unbounded quasimorphism whose quasikernel is coarsely connected is either a torus or Klein bottle bundle over a circle, or is quasiisometric to a curved (R^3,g) with hyperbolic-plane fibres.
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Outer automorphism groups and the Atiyah Conjecture
Establishes Strong Atiyah Conjecture for finite-index torsion-free subgroups of Out(G) when G is a surface group, free group or RAAG, implying discrete von Neumann dimensions and Zero Divisor Conjecture for the group algebras.