相关论文: Morphisms which are continuous on a neighborhood o…

In this short note we give a negative answer to the following open question: \emph{Let $X$ be a $\sigma$-compact paratopological group. Does there exist a continuous isomorphism of $X$ onto a topological group $G$?} Specifically, we…

We show that if $f:X\to B$ is a Lagrangian fibration from a compact connected K\"ahler hyperk\"ahler manifold $X$ onto a projective normal variety $B$, then $f$ is locally projective. This answers a question raised by L. Kamenova and…

For any genuinely ramified morphism $f\, :\, Y\, \longrightarrow\, X$ between irreducible smooth projective curves we prove that $\overline{(Y\times_X Y) \setminus \Delta}$ is connected, where $\Delta\, \subset\, Y\times_X Y$ is the…

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 this paper, we define and investigate the properties of continuous family groupoids. This class of groupoids is necessary for investigating the groupoid index theory arising from the equivariant Atiyah-Singer index theorem for families,…

We characterise proper morphisms of $\infty$-topoi in terms of a relativised notion of compactness: we show that a geometric morphism of $\infty$-topoi is proper if and only if it commutes with colimits indexed by filtered internal…

We prove a version of Gromov's compactness theorem for pseudo-holomorphic curves which holds locally in the target symplectic manifold. This result applies to sequences of curves with an unbounded number of free boundary components, and in…

The long-standing problem of the perfectness of the compactly supported equivariant homeomorphism group on a $G$-manifold (with one orbit type) is solved in the affirmative. The proof is based on an argument different than that for the case…

Using a suitable notion of principal G-bundle, defined relative to an arbitrary cartesian category, it is shown that principal bundles can be characterised as adjunctions that stably satisfy Frobenius reciprocity. The result extends from G,…

We introduce the notion of measurable bounded cohomology for measured groupoids, extending continuous bounded cohomology of locally compact groups. We show that the measurable bounded cohomology of the semidirect groupoid associated to a…

We show that any connected locally compact group which admits an expansive automorphism is nilpotent. We also show that for any locally compact group $G$, $\alpha\in {\rm Aut}(G)$ is expansive if and only if for any $\alpha$-invariant…

The concept of gyrogroups, with a weaker algebraic structure without associative law, was introduced under the background of $c$-ball of relativistically admissible velocities with Einstein velocity addition. A topological gyrogroup is just…

We prove a conjecture of Medvedev and Scanlon for endomorphisms of connected commutative linear algebraic groups $G$ defined over an algebraically closed field $\mathbb{k}$ of characteristic $0$. That is, if $\Phi\colon G\longrightarrow G$…

It is proven that the identity component of the group preserving the leaves of a generalized foliation is perfect. This shows that a well-known simplicity theorem on the diffeomorphism group extends to the nontransitive case.

We prove that every locally finite vertex-transitive graph $G$ admits a non-constant Lipschitz harmonic function.

The interplay between local consistency and global consistency has been the object of study in several different areas, including probability theory, relational databases, and quantum information. For relational databases, Beeri, Fagin,…

We show that the automorphism group of Philip Hall's universal locally finite group has ample generics,that is, it admits comeager diagonal conjugacy classes in all dimensions.Consequently, it has the small index property, is not the union…

We consider continuous extensions of minimal rotations on a locally connected compact group X by arbitrary locally compact Lie groups and prove regularity (i.e. the existence of orbit closures which project onto the whole basis X) in…

We extend the proof of automatic continuity for homeomorphism groups of manifolds to non-compact manifolds and manifolds with marked points and their mapping class groups. Specifically, we show that, for any manifold $M$ homeomorphic to the…

We prove that under some assumptions on an algebraic group $G$, indecomposable direct summands of the motive of a projective $G$-homogeneous variety with coefficients in $\mathbb{F}_p$ remain indecomposable if the ring of coefficients is…