Integral Invariants of 3-Manifolds

This note describes an invariant of rational homology 3-spheres in terms of configuration space integrals which in some sense lies between the invariants of Axelrod and Singer and those of Kontsevich.Comment: 39 pages, AMS-LaTeX, to appear in J. Diff. Geo

Configuration spaces and Vassiliev classes in any dimension

The real cohomology of the space of imbeddings of S^1 into R^n, n>3, is studied by using configuration space integrals. Nontrivial classes are explicitly constructed. As a by-product, we prove the nontriviality of certain cycles of imbeddings obtained by blowing up transversal double points in immersions. These cohomology classes generalize in a nontrivial way the Vassiliev knot invariants. Other nontrivial classes are constructed by considering the restriction of classes defined on the corresponding spaces of immersions.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-39.abs.htm

Wilson surfaces and higher dimensional knot invariants

An observable for nonabelian, higher-dimensional forms is introduced, its properties are discussed and its expectation value in BF theory is described. This is shown to produce potential and genuine invariants of higher-dimensional knots.Comment: 31 pages, 9 figure

On the naturality of the Mathai-Quillen formula

We give an alternative proof for the Mathai-Quillen formula for a Thom form using its natural behaviour with respect to fiberwise integration. We also study this phenomenon in general context.Comment: 6 page

Complex Line Bundles over Simplicial Complexes and their Applications

Discrete vector bundles are important in Physics and recently found remarkable applications in Computer Graphics. This article approaches discrete bundles from the viewpoint of Discrete Differential Geometry, including a complete classification of discrete vector bundles over finite simplicial complexes. In particular, we obtain a discrete analogue of a theorem of Andr\'e Weil on the classification of hermitian line bundles. Moreover, we associate to each discrete hermitian line bundle with curvature a unique piecewise-smooth hermitian line bundle of piecewise constant curvature. This is then used to define a discrete Dirichlet energy which generalizes the well-known cotangent Laplace operator to discrete hermitian line bundles over Euclidean simplicial manifolds of arbitrary dimension

A Note on the Equality of Algebraic and Geometric D-Brane Charges in WZW Models

The algebraic definition of charges for symmetry-preserving D-branes in Wess-Zumino-Witten models is shown to coincide with the geometric definition, for all simple Lie groups. The charge group for such branes is computed from the ambiguities inherent in the geometric definition.Comment: 12 pages, fixed typos, added references and a couple of remark

The polarization of the planet-hosting WASP-18 system

We report observations of the linear polarization of the WASP-18 system, which harbors a very massive ( approx 10 M_J) planet orbiting very close to its star with an orbital period of 0.94 days. We find the WASP-18 system is polarized at about 200 parts-per-million (ppm), likely from the interstellar medium predominantly, with no strong evidence for phase dependent modulation from reflected light from the planet. We set an upper limit of 40 ppm (99% confidence level) on the amplitude of a reflected polarized light planetary signal. We compare the results with models for a number of processes that may produce polarized light in a planetary system to determine if we can rule out any phenomena with this limit. Models of reflected light from thick clouds can approach or exceed this limit, but such clouds are unlikely at the high temperature of the WASP-18b atmosphere. Additionally, we model the expected polarization resulting from the transit of the planet across the star and find this has an amplitude of about 1.6 ppm, which is well below our detection limits. We also model the polarization due to the tidal distortion of the star by the massive planet and find this is also too small to be measured currently.Comment: 23 pages, 10 Figures, 6 Tables, Accepted to A