Related papers: Eigenvalues, K-theory and Minimal Flows

We consider two natural topologies on the space $S(X\times Y,Z)$ of all separately continuous functions defined on the product of two topological spaces $X$ and $Y$ and ranged into a topological or metric space $X$. These topologies are the…

This paper provides a full controlled version of algebraic $K$-theory. This includes a rich array of assembly maps; the controlled assembly isomorphism theorem identifying the controlled group with homology; and the stability theorem…

The work presented here emanates from questions arising from experimental observations of the propagation of surface water waves. The experiments in question featured a periodically moving wavemaker located at one end of a flume that…

In this paper we will give a structure theory for regular graphs with fixed smallest eigenvalue. As a consequence of this theory, we show that a $k$-regular graph with smallest eigenvalue $-\lambda$ has clique number linear in $k$ if $k$ is…

A flow $(X,T)$ induces the flow $(2^X,T)$. Quasifactors are minimal subsystems of $(2^X, T)$ and hence orbit closures of almost periodic points for $(2^X, T)$. We study quasifactors via the almost periodic points for $(2^X,T)$.

Let $k$ be a perfect field of positive characteristic and let $X$ be a smooth irreducible quasi-compact scheme over $k$. The Drinfeld-Kedlaya theorem states that for an irreducible $F$-isocrystal on $X$, the gap between consecutive generic…

There are two main subjects in this paper. 1) For a topological dynamical system $(X,T)$ we study the topological entropy of its "functional envelopes" (the action of $T$ by left composition on the space of all continuous self-maps or on…

Extending our results in "Entropy conjecture for continuous maps of nilmanifolds", to appear in Israel Jour. of Math., we confirm that Entropy Conjecture holds for every continuous self-map of a compact $K(\pi,1)$ manifold with the…

Let $H$ be a subnormal co-compact closed subgroup of a Hausdorff topological group $T$ and $X$ a compact Hausdorff space. We prove the inheritance theorem: A point of $X$ is almost periodic (a.p.) for $T\curvearrowright X$ iff it is a.p.…

Given a graph $F$, let $I(F)$ be the class of graphs containing $F$ as an induced subgraph. Let $W[F]$ denote the minimum $k$ such that $I(F)$ is definable in $k$-variable first-order logic. The recognition problem of $I(F)$, known as…

Given a compact Lie group $G$ acting on a space $X$, the classical Atiyah-Segal completion theorem identifies topological $K$-theory of the homotopy quotient $X/G$ with an explicit completion of $G$-equivariant topological $K$-theory of…

Unconfined granular flows along an inclined plane are investigated experimentally. During a long transient, the flow gets confined by quasistatic banks but still spreads laterally towards a well-defined asymptotic state following a…

We consider a locally path-connected compact metric space $K$ with finite first Betti number $b_1(K)$ and a flow $(K, G)$ on $K$ such that $G$ is abelian and all $G$-invariant functions $f\in\mathrm{C}(K)$ are constant. We prove that every…

Let $T$ be an o-minimal theory extending the theory of real closed ordered fields. An $H_T$-field is a model $K$ of $T$ equipped with a $T$-derivation such that the underlying ordered differential field of $K$ is an $H$-field. We study…

Equivalence classes of gapped Hamiltonians compatible with given symmetry constraints, such as those underlying topological insulators, can be defined in many ways. For the non-chiral classes modelled by vector bundles over Brillouin tori,…

We prove that the persistence diagram of the sublevel set filtration of the quadratic form f(x) = x^T M x restricted to the unit sphere S^{n-1} is analytically determined by the eigenvalues of the symmetric matrix M. By Morse theory, the…

We consider twisted equivariant K--theory for actions of a compact Lie group $G$ on a space $X$ where all the isotropy subgroups are connected and of maximal rank. We show that the associated rational spectral sequence \`a la Segal has a…

Let $K$ be a convex body in the Euclidean plane $\mathbb R^2$. We say that a point set $X \subseteq \mathbb R^2$ satsfies the property $T(K)$ if the family of translates $\{ K + x : x \in X \}$ has a line transversal. A weaker property,…

In this paper, thermal-slip coefficients in slip boundary conditions of the Stokes equation are derived using the generalized slip-flow theory, with special interest in the role of near-wall potential in micro- and nanoscale flows. As the…

Given a natural number k and an orientable surface S of finite type, define the k-curve graph to be the graph with vertices corresponding to isotopy classes of essential simple closed curves on S and with edges corresponding to pairs of…