Diguise, Containment and the \u3cem\u3ePorgy and Bess\u3c/em\u3e Revival of 1952–1956

Life in the cultural shallows tested the character of American art. Where the Depression had encouraged artists to engage in social and political criticism, the early cold war years constricted and confounded them. By conflating dissent and disloyalty, the triumphant conservatism of the cold war not only shifted the frame of cultural reference dramatically to the right, it narrowed it as well. This had a profound impact on America’s cultural establishment. With conservatives now in possession of the moral absolutes, the more politically progressive artists felt pressed into the position of endorsing ambivalence and moderation. The result, for many, was a quiet retreat from principle; unwilling to blindly adopt the conservatives’ standard of good and evil, and yet unable to risk their own, forward-thinking artists ended up chronicling rather than challenging their age. So much of fifties art became an exploration of the ordinary—domestic comedy, social commentary, “wistful melodrama,” sermons on rootlessness or delinquency or affluence—instead of a questioning of the larger truths. Tragedy, which, by challenging certitudes, required the moral commitment of liberal writers, became, in this context, anachronistic. “We are not producing real tragedy,” observed Leonard Bernstein in 1952, because “caution prevents it, all the fears prevent it; and we are left, at the moment, with an art that is rather whiling away the time until the world gets better or blows up.” Art had adopted the Technicolor blandness of the age

Groups of piecewise projective homeomorphisms

The group of piecewise projective homeomorphisms of the line provides straightforward counter-examples to the so-called von Neumann conjecture. The examples are so simple that many additional properties can be established.Comment: This version submitted to PNAS on October 22, 2012. Final version published in PNAS at http://dx.doi.org/10.1073/pnas.121842611

Equivariant measurable liftings

We discuss equivariance for linear liftings of measurable functions. Existence is established when a transformation group acts amenably, as e.g. the Moebius group of the projective line. Since the general proof is very simple but not explicit, we also provide a much more explicit lifting for semi-simple Lie groups acting on their Furstenberg boundary, using unrestricted Fatou convergence. This setting is relevant to cocycles for characteristic classes.Comment: Removed the sigma-compactness assumption from Theorem A; minor correction

A note on topological amenability

We point out a simple characterisation of topological amenability in terms of bounded cohomology, following Johnson's reformulation of amenability

French theories in IS : an exploratory study on ICIS, AMCIS and MISQ.

French theories; Information Systems Research; Actor-network theory;

Product groups acting on manifolds

We analyse volume-preserving actions of product groups on Riemannian manifolds. To this end, we establish a new superrigidity theorem for ergodic cocycles of product groups ranging in linear groups. There are no a priori assumptions on the acting groups, except a spectral gap assumption on their action. Our main application to manifolds concerns irreducible actions of Kazhdan product groups. We prove the following dichotomy: Either the action is infinitesimally linear, which means that the derivative cocycle arises from unbounded linear representations of all factors. Otherwise, the action is measurably isometric, in which case there are at most two factors in the product group. As a first application, this provides lower bounds on the dimension of the manifold in terms of the number of factors in the acting group. Another application is a strong restriction for actions of non-linear groups.Comment: To appear in the Duke Mathematical Journal; 32 pages. Minor revisions, including the addition of a variation on Theorem

The cup product of Brooks quasimorphisms

We prove the vanishing of the cup product of the bounded cohomology classes associated to any two Brooks quasimorphisms on the free group. This is a consequence of the vanishing of the square of a universal class for tree automorphism groups.Comment: 7 page

An exotic deformation of the hyperbolic space

On the one hand, we construct a continuous family of non-isometric proper CAT(-1) spaces on which the isometry group ${\rm Isom}(\mathbf{H}^{n})$ of the real hyperbolic $n$-space acts minimally and cocompactly. This provides the first examples of non-standard CAT(0) model spaces for simple Lie groups. On the other hand, we classify all continuous non-elementary actions of ${\rm Isom}(\mathbf{H}^{n})$ on the infinite-dimensional real hyperbolic space. It turns out that they are in correspondence with the exotic model spaces that we construct.Comment: 42 pages, minor modifications, this is the final versio