Related papers: Uhlenbeck compactification as a functor
We construct a category that classifies compact Hausdorff spaces by their shape and finite topological spaces by their weak homotopy type.
A stratified space is a kind of topological space together with a partition into smooth manifolds. These kinds of spaces naturally arise in the study of singular algebraic varieties, symplectic reduction, and differentiable stacks. In this…
We introduce the notion of numerical functors to generalise Eilenberg & MacLane's polynomial functors to modules over a binomial base ring. After shewing how these functors are encoded by modules over a certain ring, we record a precise…
In order to classify concordance classes of codimension 2 embeddings in a manifold M, we need to determine the complement of such an embedding. These complements are spaces over M well defined up to some homology equivalence. We construct a…
The aim of this paper (inspired from a problem of Habegger) is to describe the set of cubical decompositions of compact manifolds mod out by a set of combinatorial moves analogous to the bistellar moves considered by Pachner, which we call…
The aim of section 1 is to define the homotopic functor to category of Abelian groups, connected with the special classes of bundles with fiber matrix algebra or projective space. The aim of section 2 is to define some generalization of the…
It is shown that the quantized Teichm"uller spaces have factorization properties like those required in the definition of a modular functor.
We give a characterisation of functors whose induced functor on the level of localisations is an equivalence and where the isomorphism inverse is induced by some kind of replacements such as projective resolutions or cofibrant replacements.
Organising the relevant literature and by letting statistical convergence play the main role in the theory of compactness, a variant of compactness called statistical compactness has been achieved. As in case of sequential compactness, one…
We construct a triangulation of a compactification of the Moduli space of a surface with at least one puncture that is closely related to the Deligne-Mumford compactification. Specifically, there is a surjective map from the…
We consider the Cohen-Macaulay compactification of the space of twisted cubics in projective n-space. This compactification is the fine moduli scheme representing the functor of CM-curves with Hilbert polynomial 3t+1. We show that the…
Functor morphing provides a method to translate complex representations of automorphism groups of finite modules over finite rings to representations of automorphism groups of functors in some abelian category. In this paper we give an…
We show that the tangle space of a graph, which compactifies it, is a quotient of its Stone-\v{C}ech remainder obtained by contracting the connected components.
In the early 20th century, Laurent Schwartz observed that we can identify functions that extend smoothly to the point at infinity of one-point compactifications of Euclidean spaces. We show a similar result for a different compactification…
In the study of 2d (the space dimension) topological orders, it is well-known that bulk excitations are classified by unitary modular tensor categories. But these categories only describe the local observables on an open 2-disk in the long…
The moduli spaces of stable surfaces serve as compactifications of the moduli spaces of canonical models of smooth surfaces in the same way the moduli spaces of stable curves compactify the moduli spaces of smooth curves. However, the…
We define symmetric bundles as vector bundles in the category of symmetric spaces; it is shown that this notion is the geometric analog of the one of a representation of a Lie triple system. We show that such a bundle has an underlying…
We define a concept which we call multiplicity. First, multiplicity of a morphism is defined. Then the multiplicity of an object over another object is defined to be the minimum of the multiplicities of all morphisms from one to another.…
Compactons are solutions of the equations of motion that behave trivially outside a compact region. In general, the operators describing quantum fluctuations above compactons have singularities. However, we show that despite these…
Associated to any affine space A endowed with a metric structure of arbitrary signature we consider the space of affine functionals operating on the space of quadratic functions of A. On this functional space we characterize a symmetric…