Amenable covers and ℓ1-invisibility

Amenable Covers, Volume and L-betti Numbers of Aspherical Manifolds

We provide a proof for an inequality between volume and LBetti numbers of aspherical manifolds for which Gromov outlined a strategy based on general ideas of Connes. The implementation of that strategy involves measured equivalence relations, Gaboriau’s theory of L-Betti numbers of R-simplicial complexes, and other themes of measurable group theory. Further, we prove new vanishing theorems for ...

Teichmüller Mappings, Quasiconformal Homogeneity, and Non-amenable Covers of Riemann Surfaces

We show that there exists a universal constant Kc so that every K-strongly quasiconformally homogeneous hyperbolic surface X (not equal to H2) has the property that K > Kc > 1. The constant Kc is the best possible, and is computed in terms of the diameter of the (2, 3, 7)-hyperbolic orbifold (which is the hyperbolic orbifold of smallest area.) We further show that the minimum strong homogeneity...

THE LIMIT OF Fp-BETTI NUMBERS OF A TOWER OF FINITE COVERS WITH AMENABLE FUNDAMENTAL GROUPS

We prove an analogue of the Approximation Theorem of L-Betti numbers by Betti numbers for arbitrary coefficient fields and virtually torsionfree amenable groups. The limit of Betti numbers is identified as the dimension of some module over the Ore localization of the group ring.

Invisibility and interpretation

Invisibility is often thought to occur because of the low-level limitations of the visual system. For example, it is often assumed that backward masking renders a target invisible because the visual system is simply too slow to resolve the target and the mask separately. Here, we propose an alternative explanation in which invisibility is a goal rather than a limitation and occurs naturally whe...

Ageing and Invisibility