相关论文: Linear algebra and unification of geometries in al…

The linearisation of a second-order formulation of the conformal Einstein field equations (CEFEs) in Generalised Harmonic Gauge (GHG), with trace-free matter is derived. The linearised equations are obtained for a general background and…

In this paper we define an algebra structure on the vector space $L(\Sigma)$ generated by links in the manifold $\Sigma \times [0,1]$ where $\Sigma $ is an oriented surface. This algebra has a filtration and the associated graded algebra…

Gauged linear sigma models with (0,2) supersymmetry allow a larger choice of couplings than models with (2,2) supersymmetry. We use this freedom to find a fully linear construction of torsional heterotic compactifications, including models…

We establish some basic theorems in dimension theory and absolute extensor theory in the coarse category of metric spaces. Some of the statements in this category can be translated in general topology language by applying the Higson corona…

We consider all compatible topologies of an arbitrary finite-dimensional vector space over a non-trivial valuation field whose metric completion is a locally compact space. We construct the canonical lattice isomorphism between the lattice…

For a complete and cocomplete category $\mathcal{C}$ with a well-behaved class of `projectives' $\bar{\mathcal{P}}$, we construct a model structure on the category $s\mathcal{C}$ of simplicial objects in $\mathcal{C}$ where the weak…

The universal centralizer of a semisimple algebraic group is the family of centralizers of regular elements, parametrized by their conjugacy classes. When the group is of adjoint type, we construct a smooth, log-symplectic fiberwise…

We shall prove a convergence result relative to sequences of Minkowski symmetrals of general compact sets. In particular, we investigate the case when this process is induced by sequences of subspaces whose elements belong to a finite…

We show that many graphs naturally associated to a connected, compact, orientable surface are hierarchically hyperbolic spaces in the sense of Behrstock, Hagen and Sisto. They also automatically have the coarse median property defined by…

Motivated by analogies with basic density theorems in analytic number theory, we introduce a notion (and variations) of the homological density of one space in another. We use Weil's number field/ function field analogy to predict…

This paper unites the gauge-theoretic and hyperbolic-geometric perspectives on the asymptotic geometry of the character variety of SL(2,C) representations of a surface group. Specifically, we find an asymptotic correspondence between the…

We extend Thomason's homotopy colimit construction in the category of permutative categories to categories of algebras over an arbitrary $\Cat$ operad and analyze its properties. We then use this homotopy colimit to prove that the…

Intersection homology of Goresky and MacPherson can be defined from the Deligne sheaf, obtained from truncations of complexes of sheaves. As intersection homology is not the homology of a particular space, the search for a family of spaces…

We introduce a compactification construction for abstract quasi-local C*-algebras over countable metric spaces equipped with an isometric group action which is functorial with respect to bounded spread isomorphisms. In $1$D, the…

In this note on coarse geometry we revisit coarse homotopy. We prove that coarse homotopy indeed is an equivalence relation, and this in the most general context of abstract coarse structures. We introduce (in a geometric way) coarse…

Let $S$ be a closed orientable surface of genus at least two. We introduce a bordification of the moduli space $\mathcal{PT}(S)$ of complex projective structures, with a boundary consisting of projective classes of half-translation…

The algebras $\mathcal{L}_{g,n}(H)$ have been introduced by Alekseev-Grosse-Schomerus and Buffenoir-Roche in the middle of the 1990's, in the program of combinatorial quantization of the moduli space of flat connections over the surface…

Starting with a vertex-weighted pointed graph $(\Gamma,\mu,v_0)$, we form the free loop algebra $\mathcal{S}_0$ defined in Hartglass-Penneys' article on canonical $\rm C^*$-algebras associated to a planar algebra. Under mild conditions,…

Let X be quasi-isometric to either the mapping class group equipped with the word metric, or to Teichmuller space equipped with either the Teichmuller metric or the Weil-Petersson metric. We introduce a unified approach to study the coarse…

We consider sequences of compact Riemannian manifolds with uniform Sobolev bounds on their metric tensors, and prove that their distance functions are uniformly bounded in the H\"{o}lder sense. This is done by establishing a general trace…