Intersecting Color Manifolds

Logvinenko’s color atlas theory provides a structure in which a complete set of color-equivalent material and illumination pairs can be generated to match any given input RGB color. In chromaticity space, the set of such pairs forms a 2-dimensional manifold embedded in a 4-dimensional space. For singleilluminant scenes, the illumination for different input RGB values must be contained in all the corresponding manifolds. The proposed illumination-estimation method estimates the scene illumination based on calculating the intersection of the illuminant components of the respective manifolds through a Hough-like voting process. Overall, the performance on the two datasets for which camera sensitivity functions are available is comparable to existing methods. The advantage of the formulating the illumination-estimation in terms of manifold intersection is that it expresses the constraints provided by each available RGB measurement within a sound theoretical foundation

Dehn surgery on complicated fibered knots in the 3-sphere

Let K be a fibered knot in the 3-sphere. We show that if the monodromy of K is sufficiently complicated, then Dehn surgery on K cannot yield a lens space. Work of Yi Ni shows that if K has a lens space surgery then it is fibered. Combining this with our result we see that if K has a lens space surgery then it is fibered and the monodromy is relatively simple

A World-Volume Perspective on the Recombination of Intersecting Branes

We study brane recombination for supersymmetric configurations of intersecting branes in terms of the world-volume field theory. This field theory contains an impurity, corresponding to the degrees of freedom localized at the intersection. The Higgs branch, on which the impurity fields condense, consists of vacua for which the intersection is deformed into a smooth calibrated manifold. We show this explicitly using a superspace formalism for which the calibration equations arise naturally from F- and D-flatness.Comment: References adde

Constructing Simplicial Branched Covers

Branched covers are applied frequently in topology - most prominently in the construction of closed oriented PL d-manifolds. In particular, strong bounds for the number of sheets and the topology of the branching set are known for dimension d<=4. On the other hand, Izmestiev and Joswig described how to obtain a simplicial covering space (the partial unfolding) of a given simplicial complex, thus obtaining a simplicial branched cover [Adv. Geom. 3(2):191-255, 2003]. We present a large class of branched covers which can be constructed via the partial unfolding. In particular, for d<=4 every closed oriented PL d-manifold is the partial unfolding of some polytopal d-sphere.Comment: 15 pages, 8 figures, typos corrected and conjecture adde

Toward Realistic Intersecting D-Brane Models

We provide a pedagogical introduction to a recently studied class of phenomenologically interesting string models, known as Intersecting D-Brane Models. The gauge fields of the Standard-Model are localized on D-branes wrapping certain compact cycles on an underlying geometry, whose intersections can give rise to chiral fermions. We address the basic issues and also provide an overview of the recent activity in this field. This article is intended to serve non-experts with explanations of the fundamental aspects, and also to provide some orientation for both experts and non-experts in this active field of string phenomenology.Comment: 85 pages, 8 figures, Latex, Bibtex, v2: refs added, typos correcte

Non semi-simple sl(2) quantum invariants, spin case

Invariants of 3-manifolds from a non semi-simple category of modules over a version of quantum sl(2) were obtained by the last three authors in [arXiv:1404.7289]. In their construction the quantum parameter $q$ is a root of unity of order $2r$ where $r>1$ is odd or congruent to $2$ modulo $4$. In this paper we consider the remaining cases where $r$ is congruent to zero modulo $4$ and produce invariants of $3$-manifolds with colored links, equipped with generalized spin structure. For a given $3$-manifold $M$, the relevant generalized spin structures are (non canonically) parametrized by $H^1(M;\mathbb C/2\mathbb Z)$.Comment: 13 pages, 16 figure