Related papers: The space of generically \'etale families

Given a graph $G$, a configuration space of $G$ can be thought of as the set of all possible configurations of "robots" which can move throughout $G$, subject to some constraints. We introduce a type of configuration space which we call…

We construct infinite families of graphs that are determined by their generalized spectrum. This construction is based on new formulae for the determinant of the walk matrix of a graph. The graphs constructed here all satisfy a lower…

Let X denote either CP^m or C^m. We study certain analytic properties of the space E^n of ordered geometrically generic n-point configurations in X. This space consists of all q=(q_1,...,q_n) in X^n such that no m+1 of the points…

We give a construction of a universal average of Lie algebra elements whose exponentiation gives (when there is an associated Lie group) a totally symmetric geometric mean of Lie group elements (sufficiently closed to the identity) with the…

We work out a classification scheme for quantum modeling in Hilbert space of any kind of composite entity violating Bell's inequalities and exhibiting entanglement. Our theoretical framework includes situations with entangled states and…

Let $X$ be a nondegenerate Peano unicoherent continuum. The family $CB(X)$ of proper subcontinua of $X$ with connected boundaries is a $G_\delta$-subset of the hyperspace $C(X)$ of all subcontinua of $X$. If every nonempty open subset of…

We construct two Hilbert spaces over the set of all metrics of arbitrary but fixed signature, defined on a manifold. Every state in one of the Hilbert spaces is built of an uncountable number of wave functions representing some elementary…

Let X be a real Banach space. We prove that the existence of an injective, positive, symmetric and not strictly singular operator from X into its dual implies that either X admits an equivalent Hilbertian norm or it contains a nontrivially…

Gaussian elimination answers any question about a finitely presented vector space. However, a "uniform family" of such presentations--given as generic relations among an unspecified number of generators--is susceptible to elimination only…

We give a detailed account of the so-called "universal construction" that aims to extend invariants of closed manifolds, possibly with additional structure, to topological field theories and show that it amounts to a generalization of the…

In this paper a systematic study of the category GTS of generalized topological spaces (in the sense of H. Delfs and M. Knebusch) and their strictly continuous mappings begins. Some completeness and cocompleteness results are achieved.…

For any separated algebraic space $X/S$ we construct a separated algebraic space $\Gamma^d(X/S)$ -- the space of divided powers -- which parameterizes zero cycles of degree $d$ on $X$. The space of divided powers for an affine scheme is…

We show that for each countable simplicial complex P the following conditions are equivalent: (1) $P \in AE(X)$ iff $P \in AE(\beta X)$ for any space X; (2) There exists a P-invertible map of a metrizable compactum X with $P \in AE(X)$ onto…

It is shown that the hyperspace of all nonempty closed subsets $\Cld_{AW}(X)$ of a separable metric space $X$ endowed with the Attouch-Wets topology is homeomorphic to a separable Hilbert space if and only if the completion of $X$ is…

This is a short note on generalized $G_2$-structures obtained as a consequence of a $T$-dual construction given in a previous work of the authors together with Leonardo Soriani. Given classical $G_2$-structure on certain seven dimensional…

Let F(X,n):= X^n-\Delta be the complementary of the union \Delta of the diagonals of X^n and let U be a quotient of F(X,n) (possibly trivial) by a subgroup of the symmetric group S_n. We construct compactifications of U in products of…

For a Euclidean building $X$ of type $A_{2}$, we classify the 0-dimensional subbuildings $A$ of $\partial_{T}X$ that occur as the asymptotic boundary of closed convex subsets. In particular, we show that triviality of the holonomy of a…

Let $X$ be a smooth projective curve over an algebraically closed field $k$. Let $\mathcal{G}$ be a Bruhat-Tits group scheme on $X$ which is generically semi-simple and trivial. We show that the \'etale fundamental group of the moduli stack…

A specialization semilattice is a join semilattice together with a coarser preorder $ \sqsubseteq $ satisfying an appropriate compatibility condition. If $X$ is a topological space, then $(\mathcal P(X), \cup, \sqsubseteq )$ is a…

The Grassmannian of affine subspaces is a natural generalization of both the Euclidean space, points being zero-dimensional affine subspaces, and the usual Grassmannian, linear subspaces being special cases of affine subspaces. We show…