Related papers: Continuous Dependence on the Initial Data in the K…

Let $\mathbb{G}$ be a compact Hausdorff group acting on a compact Hausdorff space $X$, $\alpha$ an irreducible $\mathbb{G}$-representation, and $C(X)$ the $C^*$-algebra of complex-valued continuous functions on $X$. We prove that the…

Let $(M,\nabla,\langle\;,\;\rangle)$ be a manifold endowed with a flat torsionless connection $\nabla$ and a Riemannian metric $\langle\;,\;\rangle$ and $(T^kM)_{k\geq1}$ the sequence of tangent bundles given by $T^kM=T(T^{k-1}M)$ and…

It is well known that for a regular semistable curve $\mathfrak X$ over a DVR with algebraically closed residue field, the spanning trees of the dual graph of the special fiber of $\mathfrak X$ are in bijection with components of the…

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,…

Let $\Sigma$ be a closed surface, $G$ a compact Lie group, with Lie algebra $g$, and $\xi \colon P \to \Sigma$ a principal $G$-bundle. In earlier work we have shown that the moduli space $N(\xi)$ of central Yang- Mills connections, for…

The sheaf-function correspondence identifies the group of constructible functions on a real analytic manifold $M$ with the Grothendieck group of constructible sheaves on $M$. When $M$ is a finite dimensional real vector space,…

Let $V$ be a symplectic space over $\mathbb{C}$, $dim_\mathbb{C} V=2l$, and let $G$ be a finite subgroup of $Sp(V)$. The invariant regular functions $\mathbb{C}[V]^G$ inherit a Poisson algebra structure and so the quotient variety ${\cal…

Let $H$ be a pointed Hopf algebra with abelian coradical. Let $A\supseteq B$ be left (or right) coideal subalgebras of $H$ that contain the coradical of $H$. We show that $A$ has a PBW basis over $B$, provided that $H$ satisfies certain…

The celebrated Kadison--Sakai theorem states that every derivation on a von Neumann algebra is inner. In this paper, we prove this theorem for ultraweakly continuous *-\sigma-derivations, where \sigma is an ultraweakly continuous surjective…

We construct a C*-algebra that has only one irreducible representation up to unitary equivalence but is not isomorphic to the algebra of compact operators on any Hilbert space. This answers an old question of Naimark. Our construction uses…

Let $G$ be a connected reductive affine algebraic group defined over the complex numbers, and $K\subset G$ be a maximal compact subgroup. Let $X , Y$ be irreducible smooth complex projective varieties and $f: X \rightarrow Y$ an algebraic…

For a transitive Lie algebroid A on a connected manifold M and its a representation on a vector bundle F, we study the localization map Y^1: H^1(A,F)-> H^1(L_x,F_x), where L_x is the adjoint algebra at x in M. The main result in this paper…

A finite set can be supplied with a group structure which can then be used to select (classes of) differential calculi on it via the notions of left-, right- and bicovariance. A corresponding framework has been developed by Woronowicz, more…

We consider the following property of a first order theory T with a distinguished unary predicate P: every model of the theory of P occurs as the P-part of some model of T. We call this property the Gaifman property. Gaifman conjectured…

Let $f : X \rightarrow Y$ be a generically smooth nonconstant morphism between irreducible projective curves, defined over an algebraically closed field, which is \'etale on an open subset of $Y$ that contains both the singular locus of $Y$…

The study of the O(N) model at nonzero temperature is presented applying the auxiliary field method, which allows to obtain a continuous transformation between the linear and the nonlinear version of the model. In case of explicitly broken…

Transitive Lie algebroids have specific properties that allow to look at the transitive Lie algebroid as an element of the object of a homotopy functor. Roughly speaking each transitive Lie algebroids can be described as a vector bundle…

Let $A(x): =(A_{i, j}(x))$ be a continuous function defined on some subshift of $\Omega:= \{0,1, \cdots, m-1\}^\mathbb{N}$, taking $d\times d$ non-negative matrices as values and let $\nu$ be an ergodic $\sigma$-invariant measure on the…

The notions of bounded-size and quasibounded-size decompositions with bounded treedepth base classes are central to the structural theory of graph sparsity introduced by two of the authors years ago, and provide a characterization of both…

We consider Hyers-Ulam stability of a functional equation for continuous functions on a space on which a topological group acts, analogous to the additive functional equation on a group. We show, among other things, that our generalized…