The Blackwell Summer Arts Program: An Experience in Community ReVitalization

Like many American cities, Richmond, Virginia is pockmarked by once middle-class neighborhoods that have fallen into decline and are now blighted by decayed and abandoned buildings. Among the more severely depressed areas of Richmond is the historic Blackwell district. Decades ago, in an effort to provide homes for the poorest of Richmond’s citizens, row after row of nondescript, multi-family, brick-faced, public housing units or “projects” were erected in Blackwell. By the end of the 20th century, their boarded windows, crumbling infrastructures, and graffiti covered facades were sad but eloquent monuments to inefficacious governmental policies and the unrelenting poverty and despair of Blackwell’s irresolute residents

Toric Vaisman Manifolds

Vaisman manifolds are strongly related to K\"ahler and Sasaki geometry. In this paper we introduce toric Vaisman structures and show that this relationship still holds in the toric context. It is known that the so-called minimal covering of a Vaisman manifold is the Riemannian cone over a Sasaki manifold. We show that if a complete Vaisman manifold is toric, then the associated Sasaki manifold is also toric. Conversely, a toric complete Sasaki manifold, whose K\"ahler cone is equipped with an appropriate compatible action, gives rise to a toric Vaisman manifold. In the special case of a strongly regular compact Vaisman manifold, we show that it is toric if and only if the corresponding K\"ahler quotient is toric.Comment: 20 pages, update of one reference, minor change

3-manifolds efficiently bound 4-manifolds

It is known since 1954 that every 3-manifold bounds a 4-manifold. Thus, for instance, every 3-manifold has a surgery diagram. There are several proofs of this fact, including constructive proofs, but there has been little attention to the complexity of the 4-manifold produced. Given a 3-manifold M of complexity n, we show how to construct a 4-manifold bounded by M of complexity O(n^2). Here we measure ``complexity'' of a piecewise-linear manifold by the minimum number of n-simplices in a triangulation. It is an open question whether this quadratic bound can be replaced by a linear bound. The proof goes through the notion of "shadow complexity" of a 3-manifold M. A shadow of M is a well-behaved 2-dimensional spine of a 4-manifold bounded by M. We prove that, for a manifold M satisfying the Geometrization Conjecture with Gromov norm G and shadow complexity S, c_1 G <= S <= c_2 G^2 for suitable constants c_1, c_2. In particular, the manifolds with shadow complexity 0 are the graph manifolds.Comment: 39 pages, 21 figures; added proof for spin case as wel

Symplectic Lefschetz fibrations on S^1 x M^3

In this paper we classify symplectic Lefschetz fibrations (with empty base locus) on a four-manifold which is the product of a three-manifold with a circle. This result provides further evidence in support of the following conjecture regarding symplectic structures on such a four-manifold: if the product of a three-manifold with a circle admits a symplectic structure, then the three-manifold must fiber over a circle, and up to a self-diffeomorphism of the four-manifold, the symplectic structure is deformation equivalent to the canonical symplectic structure determined by the fibration of the three-manifold over the circle.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol4/paper18.abs.htm

A decomposition theorem for projective manifolds with nef anticanonical bundle

Let X be a simply connected projective manifold with nef anticanonical bundle. We prove that X is a product of a rationally connected manifold and a manifold with trivial canonical bundle. As an application we describe the MRC fibration of any projective manifold with nef anticanonical bundle