Buondì, Con colpevole ritardo vi annuncio il seminario di geometria e topologia di domani. A presto, Bruno

Orario: Giovedì 20 giugno, ore 14.30, aula seminari. Speaker: Sam Fisher (Oxford) Title: Maps to the circle, the integers, and L2-Betti numbers

Abstract: Determining conditions implying that a manifold fibers over the circle is an old and interesting problem. One of the most celebrated results in this direction is Agol's theorem, which states that every hyperbolic 3-manifold has a finite cover that fibers over the circle. In higher dimensions, much less is known. Recently, Italiano--Martelli--Migliorini gave the first example of a (cusped) hyperbolic 5-manifold fibering over the circle, answering open questions in topology and geometric group theory. Hyperbolic 3-manifolds and the IMM example are examples of hyperbolic manifolds whose fundamental groups act geometrically on CAT(0) cube complexes and consequentially have RFRS fundamental group. In this talk, we will discuss an algebraic version of the fibering problem: a group algebraically fibers if it maps onto the integers with finitely generated kernel. In the class of RFRS groups, we will see that finiteness properties of the kernel are controlled by vanishing of L2-invariants. We will also discuss applications of these results to high-dimensional hyperbolic manifolds