相关论文: Some universal properties of Levin-Wen models
In an earlier paper (math.NT/9906019) we showed that any integral unimodular lattice L of rank n which is not isometric with Z^n has a characteristic vector of norm at most n-8. [A "characteristic vector" of L is a vector w in L such that…
We give lower bounds, in terms of the Euler characteristic, for the $L^2$-norm of the Weyl curvature of closed Riemannian 4-manifolds. The same bounds were obtained by Gursky, in the case of positive scalar curvature metrics.
In this paper we describe how relativistic field theories containing defects are equivalent to a class of boundary field theories. As a consequence previously derived results for boundaries can be directly applied to defects, these results…
We generalize our previous lattice construction of the abelian bosonization duality in $2+1$ dimensions to the entire web of dualities as well as the $N_f=2$ self-duality, via the lattice implementation of a set of modular transformations…
We prove two results about vector bundles on singular algebraic surfaces. First, on proper surfaces there are vector bundles of rank two with arbitrarily large second Chern number and fixed determinant. Second, on separated normal surfaces…
Let G be a simple Lie group of real rank one, and S the ideal boundary of the corresponding symmetric space of noncompact type (H^n_R, H^n_C, H^n_H or H^2_O). We show the finiteness of the possible values of the secondary characteristic…
In this talk, we summarize the collider phenomenology and recent experimental results for various models of extra dimensions, including the large extra dimensions (ADD model), warped extra dimensions (Randall-Sundrum model),…
Given an affine variety X and a finite dimensional vector space of regular functions L on X, we associate a convex body to (X, L) such that its volume is responsible for the number of solutions of a generic system of functions from L. This…
We study varieties generated by semi-primal lattice-expansions by means of category theory. We provide a new proof of the Keimel-Werner topological duality for such varieties and, using similar methods, establish its discrete version. We…
We construct and investigate certain (unbalanced) superalgebra structures on $\text{End}_K(V)$, with $K$ a field of characteristic $0$ and $V$ a finite dimensional $K$-vector space (of dimension $n\geq 2$). These structures are induced by a…
This paper presents some possible features of general expressions for Lovelock tensors and for the coefficients of Lovelock Lagrangians up to the 15th order in curvature (and beyond) in terms of the Riemann-Christoffel and Ricci curvature…
In this note we show that Voevodsky's univalence axiom holds in the model of type theory based on symmetric cubical sets. We will also discuss Swan's construction of the identity type in this variation of cubical sets. This proves that we…
We develop a framework that systematically casts the solvability and uniqueness conditions of linearized geometric boundary-value problems into cohomological terms. The theory is designed to be applicable without assumptions on the…
We establish an isomorphism between certain complex-valued and vector-valued modular form spaces of half-integral weight, generalizing the well-known isomorphism between modular forms for $\Gamma_0(4)$ with Kohnen's plus condition and…
We present a unified and completely general formulation of extended geometry, characterised by a Kac-Moody algebra and a highest weight coordinate module. Generalised diffeomorphisms are constructed, as well as solutions to the section…
Generalized differential forms are used in discussions of metric geometries and Einstein's vacuum field equations. Cartan's structure equations are generalized and applied. In particular flat generalized connections are associated with any…
Warped configurations admitting pairs of gravitating defects are analyzed. After devising a general method for the construction of multidefects, specific examples are presented in the case of higher-dimensional Einstein-Hilbert gravity. The…
We present a series of results, including local characterizations of $(\lambda,m+n)$-Einstein metrics in the context of warped product Einstein spaces. Using these local properties, we restate already known global characterizations of…
A domain in $\C^n$ with Levi-flat boundary near a given point is characterized in terms of the boundary behavior of the Kobayashi or Bergman metrics, or of the Bergman kernel. Some results are given in the case of intermediate values of the…
We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…