Related papers: Nonvanishing vector fields on orbifolds

In this paper we characterize the compact orbifolds, quotients $ X = \mathcal{D} /\Gamma$ of a bounded symmetric domain $ \mathcal{D}$ of tube type by the action of a discontinuous group $\Gamma$, as those projective orbifolds with ample…

Finite-order invariants of knots in arbitrary 3-manifolds (including non-orientable ones) are constructed and studied by methods of the topology of discriminant sets. Obstructions to the integrability of admissible weight systems to…

This is partly a survey and partly a research article. Some known results and open problems about Kaehler groups (fundamental groups of compact Kaehler manifolds) are discussed. A new notion of Kaehler homomorphism is introduced. This is a…

We study orbifolds of two-dimensional topological field theories using defects. If the TFT arises as the twist of a superconformal field theory, we recover results on the Neveu-Schwarz and Ramond sectors of the orbifold theory as well as…

We introduce the \Gamma-extension of the spectrum of the Laplacian of a Riemannian orbifold, where \Gamma is a finitely generated discrete group. This extension, called the \Gamma-spectrum, is the union of the Laplace spectra of the…

Obstruction flatness of a strongly pseudoconvex hypersurface $\Sigma$ in a complex manifold refers to the property that any (local) K\"ahler-Einstein metric on the pseudoconvex side of $\Sigma$, complete up to $\Sigma$, has a potential…

While vector-valued automorphic forms can be defined for an arbitrary Fuchsian group $\Gamma$ and an arbitrary representation $R$ of $\Gamma$ in GL$(n,{\mathbb C})$, their existence has been established in the literature only when…

We present a systematic study of non-supersymmetric type II toroidal asymmetric orbifolds with vanishing vacuum energy at one-loop in string perturbation theory. These are engineered through the conservation of a supercharge-like operator…

Scalar fields with non-trivial kinetic term derived from a nonlinear sigma model are motivated by UV completions of gravity such as string theory. We discuss the $\mathrm{SL}(2,\mathbb{R})$ and $\mathrm{O}(3)$ sigma models with interacting…

We investigate the open Closing Lemma problem for vector fields on the 2-dimensional torus. Under the assumption of bounded type rotation number, the $C^r$ Closing Lemma is verified for smooth vector fields that are area-preserving at all…

Every isometry $\sigma$ of a positive-definite even lattice $Q$ can be lifted to an automorphism of the lattice vertex algebra $V_Q$. An important problem in vertex algebra theory and conformal field theory is to classify the…

This note provides an affirmative answer to a question of Viterbo concerning the existence of nondiffeomorphic contact forms that share the same Reeb vector field. Starting from an observation by Croke-Kleiner and Abbondandolo that such…

This paper presents a generalisation of Sylvester's law of inertia to real non-degenerate quadratic forms on a fixed real vector bundle over a connected locally connected paracompact Hausdorff space. By interpreting the classical inertia as…

The partition function of an N=2 gauge theory in the Omega-background satisfies, for generic value of the parameter beta=-eps_1/eps_2, the, in general extended, but otherwise beta-independent, holomorphic anomaly equation of special…

The local Euler obstructions and the Euler characteristics of linear sections with all hyperplanes on a stratified projective variety are key geometric invariants in the study of singularity theory. Despite their importance, in general it…

Let k be any global field of characteristic not 2. We construct a k-variety X such that X(k) is empty, but for which the emptiness cannot be explained by the Brauer-Manin obstruction or even by the Brauer-Manin obstruction applied to finite…

We present a model of vacuum tunneling through a classically forbidden region where a scalar field changes its value simultaneously over the entire volume of a (meta)stable ancestor vacuum with spherical curvature. The tunneling leaves the…

The long-range fields associated with non-abelian vortices generally obstruct full realization, in the spectrum, of the symmetry of the ground state. In the context of 2+1 dimensional field theories, we show how this effect manifests itself…

We analyze the obstruction to metrics of positive scalar curvature within a given bounded distortion class of metrics. This obstruction lives in a non-Hausdorff cohomology group Poincare dual to the uniformly finite homology studied by…

We study the process of quantum tunnelling in scalar-tensor theories in which the scalar field is non-minimally coupled to gravity. In these theories gravitational instantons can deviate substantially from sphericity and can in fact develop…