Related papers: The Cichon diagram
We first review the three known chiral anomalies in four dimensions and then use the anomaly free conditions to study the uniqueness of quark and lepton representations and charge quantizations in the standard model. We also extend our…
We develop an explicit covering theory for complexes of groups, parallel to that developed for graphs of groups by Bass. Given a covering of developable complexes of groups, we construct the induced monomorphism of fundamental groups and…
In this paper, we introduce a flip operation on self-complementary ideals of chain product posets and study the resulting flip graphs. We give asymptotics for the number of vertices in these graphs, compute their diameters, and give bounds…
In this paper the necessary and sufficient conditions for a mapping to be the dependence of the complete solution of some differentiable first-order ordinary differential equation on the initial Cauchy condition are deduced. The result is…
We prove that the problem of counting the number of colourings of the vertices of a graph with at most two colours, such that the colour classes induce connected subgraphs is #P-complete. We also show that the closely related problem of…
We study local normal forms for completely integrable systems on Poisson manifolds in the presence of additional symmetries. The symmetries that we consider are encoded in actions of compact Lie groups. The existence of Weinstein's…
An introduction to the theory of bundle gerbes and their relationship to Hitchin-Chatterjee gerbes is presented. Topics covered are connective structures, triviality and stable isomorphism as well as examples and applications.
We give an introduction to constructive category theory by answering two guiding computational questions. The first question is: how do we compute the set of all natural transformations between two finitely presented functors like…
We give a characterization of the ''uniform closure'' of the dual of a $C^{*}$-algebra. Some applications in harmonic analysis are given.
We propose to extend ``invertibility'' to ``regularity'' for categories in general abstract algebraic manner. Higher regularity conditions and ``semicommutative'' diagrams are introduced. Distinction between commutative and…
The central topic of this thesis is the study of some properties of a class of complex compact manifolds~: Moishezon manifolds. In the first part, we generalize J.-P. Demailly's holomorphic Morse inequalities to the case of a line bundle…
Leech's (co)homology groups of finite cyclic monoids are computed.
Addition chains are a classical construction for fast exponentiation and related computation problems. In this paper, we study a chain for a fixed integer $n$ by decomposing each generator into a \emph{determiner} and a \emph{regulator}…
We investigate supersymmetric QCD with N_c+1 flavors using an extension of the recently proposed relation between gauge theories and matrix models. The impressive agreement between the two sides provides a beautiful confirmation of the…
From a procedure to calculate the $C_5$-cone of a reduced complex analytic curve $X \subset \mathbb{C}^n$ at a singular point $0 \in X$, we extract a collection of integers that we call {\it auxiliary multiplicities} and we prove they…
In the enriched setting, the notions of injective and projective model structures on a category of enriched diagrams also make sense. In this paper, we prove the existence of these model structures on enriched diagram categories under local…
Every definably complete expansion of an ordered field satisfies an analogue of the Baire Category Theorem.
We define a coherent adjunction in a strict $3$-category and we use string diagrams to show that any adjunction can be extended to a coherent adjunction in an essentially unique way.
This paper introduces a new systematic algorithm for constructing periodic Euclidean weaving diagrams with combinatorial arguments. It is shown that such a weaving diagram can be considered as a specific type of four-regular periodic planar…
Let $R$ be a commutative ring $R$ with $1_R$ and with group of units $R^{\times}$. Let $\Phi = \Phi(t_1,\ldots, t_h) = \sum_{i=1}^h \varphi_it_i$ be an $h$-ary linear form with nonzero coefficients $\varphi_1,\ldots, \varphi_h \in R$. Let…