Related papers: Compactness and compactifications in generalized t…

In a classical paper by Ben-David and Magidor, a model of set theory was exhibited in which $\aleph_{\omega+1}$ carries a uniform ultrafilter that is $\theta$-indecomposable for every uncountable cardinal $\theta<\aleph_\omega$. In this…

The possibility of extending operations of topological and semitopological algebras to their Stone-\v{C}ech compactification and factorization of continuous functions through homomorphisms to metrizable algebras are investigated. Most…

We study the process of compactification as a topology change. It is shown how the mediating spacetime topology, or cobordism, may be simplified through surgery. Within the causal Lorentzian approach to quantum gravity, it is shown that any…

In this paper, we use new results together with established facts about Thurston's compactification of Teichm\"uller space to address the geometric P=W conjecture for $\mathrm{SL}(2,\mathbb{C})$, which concerns projective compactifications…

We show relative to strong hypotheses that patterns of compact cardinals in the universe, where a compact cardinal is one which is either strongly compact or supercompact, can be virtually arbitrary. Specifically, we prove if V is a model…

We study a number of local and global classification problems in generalized complex geometry. In the first topic, we characterize the local structure of generalized complex manifolds by proving that a generalized complex structure near a…

Let $X$ be a locally compact topological space, $(Y,d)$ be a boundedly compact metric space and $LB(X,Y)$ be the space of all locally bounded functions from $X$ to $Y$. We characterize compact sets in $LB(X,Y)$ equipped with the topology of…

Group Field Theories (GFT) are quantum field theories over group manifolds; they can be seen as a generalization of matrix models. GFT Feynman graphs are tensor graphs generalizing ribbon graphs (or combinatorial maps); these graphs are…

We expand upon a claim made in a recent paper [arXiv:1411.5721] that generic minimally supersymmetric AdS backgrounds of warped flux compactifications of Type II and M theory can be understood as satisfying a straightforward weak…

We study problems concerning the Samuel compactification of the automorphism group of a countable first-order structure. A key motivating question is a problem of Furstenberg and a counter-conjecture by Pestov regarding the difference…

In this article, we introduce the notion of mutation semigroup algebras. This concept simultaneously generalizes cluster algebras and semigroup algebras. We show that, under some mild conditions on the singularities, the spectrum $U={\rm…

We study the $3d$ $\mathcal{N}=2$ theories resulting from the compactification of a family of $5d$ SCFTs on a torus with flux in the global symmetry. The family of $5d$ SCFTs used in the analysis is the one that UV completes the $5d$…

Let a group $\Gamma$ act on a paracompact, locally compact, Hausdorff space $M$ by homeomorphisms and let $2^M$ denote the set of closed subsets of $M$. We endow $2^M$ with the Chabauty topology, which is compact and admits a natural…

A new transparent proof of the well known good compactification theorem for the complex torus $(\Bbb C^*)^n$ is presented. This theorem provides a powerful tool in enumerative geometry for subvarieties in the complex torus. The paper also…

We prove that if there are $\mathfrak c$ incomparable selective ultrafilters then, for every infinite cardinal $\kappa$ such that $\kappa^\omega=\kappa$, there exists a group topology on the free Abelian group of cardinality $\kappa$…

A convenient bicategory of topological stacks is constructed which is both complete and Cartesian closed. This bicategory, called the bicategory of compactly generated stacks, is the analogue of classical topological stacks, but for a…

Condensed mathematics, developed by Clausen and Scholze over the last few years, proposes a generalization of topology with better categorical properties. It replaces the concept of a topological space by that of a condensed set, which can…

To every singular reduced projective curve X one can associate many fine compactified Jacobians, depending on the choice of a polarization on X, each of which yields a modular compactification of a disjoint union of the generalized Jacobian…

Let $K$ be a countable field. Then $K$ is large in the sense of Pop if and only if it admits a field topology which is "generalized t-henselian" (gt-henselian) in the sense of Dittmann, Walsberg, and Ye, meaning that the implicit function…

In this article, we study the variation of the Gieseker and Uhlenbeck compactifications of the moduli spaces of Mumford-Takemoto stable vector bundles of rank 2 by changing polarizations. Some {\it canonical} rational morphisms among the…