AdS/CFT Correspondence and Type 0 String Theory

We review some applications of Type 0 string theory in the context of the AdS/CFT correspondence.Comment: 6 pages, LaTeX + JHEP.cls, talk presented at the TMR conference ``Quantum aspects of gauge theories, supersymmetry and unification'', Paris, September 1-7, 199

Links, two-handles, and four-manifolds

We show that only finitely many links in a closed 3-manifold share the same complement, up to twists along discs and annuli. Using the same techniques, we prove that by adding 2-handles on the same link we get only finitely many smooth cobordisms between two given closed 3-manifolds. As a consequence, there are finitely many smooth closed 4-manifolds constructed from some Kirby diagram with bounded number of crossings, discs, and strands, or from some Turaev special shadow with bounded number of vertices. (These are the 4-dimensional analogues of Heegaard diagrams and special spines for 3-manifolds.) We therefore get two filtrations on the set of all smooth closed 4-manifolds with finite sets. The two filtrations are equivalent after linear rescalings, and their cardinality grows at least as n^{c*n}.Comment: 23 pages, 9 figures. Final versio

Hyperbolic three-manifolds that embed geodesically

We prove that every complete finite-volume hyperbolic 3-manifold $M$ that is tessellated into right-angled regular polyhedra (dodecahedra or ideal octahedra) embeds geodesically in a complete finite-volume connected orientable hyperbolic 4-manifold $W$, which is also tessellated into right-angled regular polytopes (120-cells and ideal 24-cells). If $M$ is connected, then Vol($W$) < $2^{49}$Vol($M$). This applies for instance to the Whitehead and the Borromean links complements. As a consequence, the Borromean link complement bounds geometrically a hyperbolic 4-manifold.Comment: 11 pages, 6 figures. Minor corrections from the previous version

The Role of Mindfulness in the Regulation of Behavior Among Those Prone to Negative Urgency

Negative emotions can be challenging to regulate, and for some individuals can lead to failures of behavior regulation. The present study is an initial effort to explore the role that mindfulness may play in fostering effective behavior regulation among those prone to high negative urgency (NU). Eighty undergraduate students were recruited based on their high or low scores of NU. First, participants completed a self-report measure of mindfulness (Mindful Attention Awareness Scale; MAAS), an Emotional Go/No Go task in an fMRI scanner, and then reported alcohol consumption. Results showed that those with high in NU had low levels of mindfulness compared to those low in NU. Mindfulness predicted substance use at the one- month follow-up after controlling for the predictive roles of NU and gender. Further exploration of the underlying neural mechanisms of mindfulness is needed to better understand its impact on emotion- and self-regulatory processes, especially during difficult emotional experience

Hyperbolic Dehn filling in dimension four

We introduce and study some deformations of complete finite-volume hyperbolic four-manifolds that may be interpreted as four-dimensional analogues of Thurston's hyperbolic Dehn filling. We construct in particular an analytic path of complete, finite-volume cone four-manifolds $M_t$ that interpolates between two hyperbolic four-manifolds $M_0$ and $M_1$ with the same volume $\frac {8}3\pi^2$. The deformation looks like the familiar hyperbolic Dehn filling paths that occur in dimension three, where the cone angle of a core simple closed geodesic varies monotonically from $0$ to $2\pi$. Here, the singularity of $M_t$ is an immersed geodesic surface whose cone angles also vary monotonically from $0$ to $2\pi$. When a cone angle tends to $0$ a small core surface (a torus or Klein bottle) is drilled producing a new cusp. We show that various instances of hyperbolic Dehn fillings may arise, including one case where a degeneration occurs when the cone angles tend to $2\pi$, like in the famous figure-eight knot complement example. The construction makes an essential use of a family of four-dimensional deforming hyperbolic polytopes recently discovered by Kerckhoff and Storm.Comment: 60 pages, 23 figures. Final versio

Countable groups are mapping class groups of hyperbolic 3-manifolds

We prove that for every countable group G there exists a hyperbolic 3-manifold M such that the isometry group of M, the mapping class group of M, and the outer automorphism group of the fundamental group of M are isomorphic to G.Comment: 15 pages, 6 figure