Related papers: Singular topologies in the Boulatov model
Even though flt is a number theoretic result we prove that the result depends on the topological as well as the field structure of the underlying space.
Over a large class of function fields, we show that the solutions of some linear equations in the topological closure of a certain subgroup of the group of units in the function field are exactly the solutions that are already in the…
A new topological field theory is constructed, which is characterized by cubic interactions similar to those of non-abelian Chern-Simons field theories, but still retains the simplicity of the abelian case. The perturbative expansion of…
We use a reformulation of topological group field theories in 3 and 4 dimensions in terms of variables associated to vertices, in 3d, and edges, in 4d, to obtain new scaling bounds for their Feynman amplitudes. In both 3 and 4 dimensions,…
Basic concepts and definitions in differential geometry and topology which are important in the theory of solitons and instantons are reviewed. Many examples from soliton theory are discussed briefly, in order to highlight the application…
In this article, we introduce an interesting topology-like concept concerning groups (and with almost the same method it can be defined for other algebraic systems). Given an arbitrary group $G$, we define a {\em topo-system} on $G$ as a…
We give model-independent arguments, valid in nearly any number of spacetime dimensions, that topological solitons and instantons satisfy Bogomol'nyi-type bounds and, when these bounds are saturated, satisfy self-duality equations. In the…
Over the past few years there has been considerable progress in the structural understanding of special Colombeau algebras. We present some of the main trends in this development: non-smooth differential geometry, locally convex theory of…
We discuss the notion of symmetries in non-local field theories characterized by integro-differential equations of motion, from a geometric perspective. We then focus on Group Field Theory (GFT) models of quantum gravity and provide a…
In the last two decades there was a lot of progress in understanding the geometry of smooth Gaussian fields. This survey aims to cover one particular line of research: the large scale behaviour of level and excursion sets and their…
If a scalar field theory in (1+1) dimensions possesses soliton solutions obeying first order BPS equations, then, in general, it is possible to find an infinite number of related field theories with BPS solitons which obey closely related…
In this paper, using some properties of fundamental groups and covering spaces of connected polyhedra and CW-complexes, we present topological proof for some famous theorems about finitely presented groups.
We present new classes of permutation polynomials over finite fields.
By introducing various topologies on the homotopy groups of a topological space, some researchers make these well known notions in algebraic topology more useful and powerful. In this paper, first we recall and review some known topologies…
This paper surveys some results and methods in topological transformation groups.
These notes are devoted to explaining aspects of the mirror manifold problem that can be naturally understood from the point of view of topological field theory. Basically this involves studying the topological field theories made by…
We survey recent applications of topology and singularity theory in the study of the algebraic complexity of concrete optimization problems in applied algebraic geometry and algebraic statistics.
We introduce the group field theory formalism for quantum gravity, mainly from the point of view of loop quantum gravity, stressing its promising aspects. We outline the foundations of the formalism, survey recent results and offer a…
We develop the deformation theory of cohomological field theories (CohFTs), which is done as a special case of a general deformation theory of morphisms of modular operads. This leads us to introduce two new natural extensions of the notion…
We present a category theoretical generalization of the Goussarov theorem for finite type invariants, relating generating sets for generalized finite type theories with diagrams systems for the corresponding topological objects. We will…